## Pillichshammer, Friedrich

Compute Distance To:
 Author ID: pillichshammer.friedrich Published as: Pillichshammer, Friedrich; Pillichshammer, F. External Links: MGP · ORCID · Wikidata · GND · IdRef
 Documents Indexed: 153 Publications since 2000, including 2 Books 4 Contributions as Editor Co-Authors: 52 Co-Authors with 133 Joint Publications 953 Co-Co-Authors
all top 5

### Co-Authors

 23 single-authored 44 Dick, Josef 43 Kritzer, Peter 20 Larcher, Gerhard 16 Leobacher, Gunther 10 Hinrichs, Aicke 9 Pirsic, Isabel 8 Wasilkowski, Grzegorz W. 8 Woźniakowski, Henryk 7 Faure, Henri 6 Kritzinger, Ralph 6 Winterhof, Arne 5 Irrgeher, Christian 4 Baldeaux, Jan 4 Hofer, Roswitha 4 Niederreiter, Harald 3 Schmid, Wolfgang Ch. 2 Drmota, Michael 2 Gomez-Perez, Domingo 2 Greslehner, Julia 2 Hellekalek, Peter 2 Markhasin, Lev 2 Nuyens, Dirk 2 Plaskota, Leszek 2 Scheicher, Klaus 2 Sonnleitner, Mathias 2 Suzuki, Kosuke 2 Tichy, Robert Franz 2 Ullrich, Mario 2 Waterhouse, Benjamin J. 2 Xing, Chaoping 2 Yoshiki, Takehito 1 Aistleitner, Christoph 1 Bilyk, Dmitry 1 Buckwar, Evelyn 1 Burgstaller, Bernhard 1 Doerr, Benjamin 1 Ebert, Adrian 1 Gnewuch, Michael 1 Gomez, Ana Isabel 1 Grabner, Peter J. 1 Hofinger, Andreas 1 Krizer, Peter 1 Kuo, Frances Y. 1 Laimer, Helene 1 Larchner, Gerhard 1 Neumüller, Mario 1 Prochno, Joscha 1 Saad Eddin, Sumaia 1 Schell, Thomas 1 Sloan, Ian Hugh 1 Steinerberger, Stefan 1 Tezuka, Shu
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### Serials

 23 Journal of Complexity 11 Uniform Distribution Theory 8 Acta Arithmetica 7 Monatshefte für Mathematik 6 Mathematics of Computation 6 Archiv der Mathematik 5 Journal of Computational and Applied Mathematics 5 Finite Fields and their Applications 4 Bulletin of the Australian Mathematical Society 4 Functiones et Approximatio. Commentarii Mathematici 4 Journal of Approximation Theory 4 Mathematics and Computers in Simulation 3 Journal of Number Theory 3 Numerische Mathematik 3 SIAM Journal on Numerical Analysis 3 Numerical Algorithms 3 Journal de Théorie des Nombres de Bordeaux 2 American Mathematical Monthly 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Computing 2 Mathematika 2 Proceedings of the American Mathematical Society 2 Quaestiones Mathematicae 2 Mathematica Pannonica 2 Monte Carlo Methods and Applications 2 Radon Series on Computational and Applied Mathematics 1 Discrete Mathematics 1 IMA Journal of Numerical Analysis 1 Israel Journal of Mathematics 1 BIT 1 The Fibonacci Quarterly 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Sitzungsberichte. Abteilung II. Österreichische Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse 1 Rendiconti di Matematica e delle sue Applicazioni. Serie VII 1 Acta Mathematica Hungarica 1 Constructive Approximation 1 Internationale Mathematische Nachrichten 1 Elemente der Mathematik 1 Indagationes Mathematicae. New Series 1 Integers 1 International Journal of Number Theory 1 Compact Textbooks in Mathematics
all top 5

### Fields

 114 Number theory (11-XX) 78 Numerical analysis (65-XX) 17 Approximations and expansions (41-XX) 7 Convex and discrete geometry (52-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Functional analysis (46-XX) 6 Probability theory and stochastic processes (60-XX) 5 General and overarching topics; collections (00-XX) 4 Geometry (51-XX) 3 Computer science (68-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Information and communication theory, circuits (94-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Operator theory (47-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Mathematics education (97-XX)

### Citations contained in zbMATH Open

129 Publications have been cited 1,144 times in 456 Documents Cited by Year
Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012
Dick, Josef; Pillichshammer, Friedrich
2010
Introduction to quasi-Monte Carlo integration and applications. Zbl 1309.65006
Leobacher, Gunther; Pillichshammer, Friedrich
2014
Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021
Dick, Josef; Pillichshammer, Friedrich
2005
Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007
Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H.
2005
Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077
Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk
2011
Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Approximation of analytic functions in Korobov spaces. Zbl 1342.41021
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich
2014
Integration in Hermite spaces of analytic functions. Zbl 1316.65034
Irrgeher, Christian; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2015
The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J.
2008
Tractability of multivariate analytic problems. Zbl 1333.65019
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2016
Distribution properties of generalized van der Corput-Halton sequences and their subsequences. Zbl 1188.11038
Hofer, Roswitha; Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
2009
Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich
2007
Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. Zbl 1244.65002
Baldeaux, Jan; Dick, Josef; Leobacher, Gunther; Nuyens, Dirk; Pillichshammer, Friedrich
2012
Optimal $$\mathcal {L}_{2}$$ discrepancy bounds for higher order digital sequences over the finite field $$\mathbb {F}_{2}$$. Zbl 1294.11127
Dick, Josef; Pillichshammer, Friedrich
2014
On the mean square weighted $${\mathcal L}_2$$ discrepancy of randomized digital $$(t,m,s)$$-nets over $${\mathbb Z}_2$$. Zbl 1080.11058
Dick, Josef; Pillichshammer, Friedrich
2005
Approximation in Hermite spaces of smooth functions. Zbl 1338.65040
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2016
$$L_2$$ discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Zbl 1198.11072
Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb; Schmid, Wolfgang Ch.
2010
Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086
Dick, Josef; Pillichshammer, Friedrich
2014
Sums of distances to the nearest integer and the discrepancy of digital nets. Zbl 1054.11039
Larcher, G.; Pillichshammer, F.
2003
Walsh series analysis of the $$L_2$$-discrepancy of symmetrized point sets. Zbl 1108.11309
Larcher, G.; Pillichshammer, F.
2001
Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2005
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
Dick, Josef; Pillichshammer, Friedrich
2014
Precise distribution properties of the van der Corput sequence and related sequences. Zbl 1088.11060
Drmota, Michael; Larcher, Gerhard; Pillichshammer, Friedrich
2005
From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063
Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich
2015
Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
2016
Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich
2011
On the discrepancy of $$(0,1)$$-sequences. Zbl 1048.11061
Pillichshammer, Friedrich
2004
On the $$L_p$$-discrepancy of the Hammersley point set. Zbl 1010.11043
Pillichshammer, Friedrich
2002
Bounds for the weighted $$L^p$$ discrepancy and tractability of integration. Zbl 1366.11090
Leobacher, Gunther; Pillichshammer, Friedrich
2003
Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich
2006
The weighted star discrepancy of Korobov’s $$p$$-sets. Zbl 1329.11078
Dick, Josef; Pillichshammer, Friedrich
2015
An exact formula for $$L_2$$ discrepancy of the shifted Hammersley point set. Zbl 1147.11041
Kritzer, Peter; Pillichshammer, Friedrich
2006
A note on equivalence of anchored and ANOVA spaces; lower bounds. Zbl 1355.65027
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
2017
Optimal order of $$L_p$$-discrepancy of digit shifted Hammersley point sets in dimension 2. Zbl 1340.11062
Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich
2015
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich
2015
A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Zbl 1150.11026
Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
2007
A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Zbl 1300.65004
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2015
Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003
Dick, Josef; Pillichshammer, Friedrich
2005
$$L_p$$ discrepancy of generalized two-dimensional Hammersley point sets. Zbl 1175.11042
Faure, Henri; Pillichshammer, Friedrich
2009
Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030
Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich
2008
Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006
Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich
2008
$$L_p$$-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070
Kritzinger, Ralph; Pillichshammer, Friedrich
2015
On the sum of squared distances in the Euclidean plane. Zbl 0966.52007
Pillichshammer, Friedrich
2000
On the existence of higher order polynomial lattices based on a generalized figure of merit. Zbl 1130.65047
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Schmid, Wolfgang Ch.
2007
Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2011
Tractability properties of the weighted star discrepancy. Zbl 1146.65002
Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch.
2008
The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002
Cristea, Ligia L.; Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2007
A note on the sum of distances under a diameter constraint. Zbl 1002.51015
Pillichshammer, Friedrich
2001
Polynomial lattice point sets. Zbl 1294.11129
Pillichshammer, Friedrich
2012
Construction algorithms for good extensible lattice rules. Zbl 1247.11100
Niederreiter, Harald; Pillichshammer, Friedrich
2009
$$L_2$$ discrepancy of two-dimensional digitally shifted Hammersley point sets in base $$b$$. Zbl 1228.11122
Faure, Henri; Pillichshammer, Friedrich
2009
Optimal $$L_{p}$$-discrepancy bounds for second order digital sequences. Zbl 1394.11060
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2017
$$\mathbb{L}_\infty$$-approximation in Korobov spaces with exponential weights. Zbl 1367.41024
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2017
Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034
Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
2019
Constructions of general polynomial lattices for multivariate integration. Zbl 1125.65006
Kritzer, Peter; Pillichshammer, Friedrich
2007
Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088
Pillichshammer, Friedrich; Steinerberger, Stefan
2009
On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953
Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich
2018
Low discrepancy polynomial lattice point sets. Zbl 1256.11042
Kritzer, Peter; Pillichshammer, Friedrich
2012
Moments of the weighted sum-of-digits function. Zbl 1092.11007
Larcher, Gerhard; Pillichshammer, Friedrich
2005
Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich
2006
Uniform distribution of sequences connected with the weighted sum-of-digits function. Zbl 1201.11081
Pillichshammer, Friedrich
2007
On extremal point disributions in the Euclidean plane. Zbl 1026.52008
Pillichshammer, F.
2003
Points sets with low $$L_p$$ discrepancy. Zbl 1153.11037
Kritzer, Peter; Pillichshammer, Friedrich
2007
The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J.
2007
A note on optimal point distributions in $$[0,1)^{s}$$. Zbl 1201.11084
Larcher, Gerhard; Pillichshammer, Friedrich
2007
Distribution properties of sequences generated by $$Q$$-additive functions with respect to Cantor representation of integers. Zbl 1228.11114
Hofer, Roswitha; Pillichshammer, Friedrich; Pirsic, Gottlieb
2009
A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086
Larcher, Gerhard; Pillichshammer, Friedrich
2014
Uniform distribution and quasi-Monte Carlo methods. Discrepancy, integration and applications. Based on invited talks of the workspop, Linz, Austria, October 14–18, 2013. Zbl 1291.11003
2014
Truncation dimension for function approximation. Zbl 1405.65021
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W.
2018
Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152
Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu
2019
On Weyl products and uniform distribution modulo one. Zbl 1410.11106
Aistleitner, Christoph; Larcher, Gerhard; Pillichshammer, Friedrich; Eddin, Sumaia Saad; Tichy, Robert F.
2018
Improved upper bounds for the star discrepancy of digital nets in dimension 3. Zbl 1054.11040
Pillichshammer, Friedrich
2003
A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2010
The $$p$$-adic diaphony of the Halton sequence. Zbl 1282.11087
Pillichshammer, Friedrich
2013
On the existence of low-diaphony sequences made of digital sequences and lattice point sets. Zbl 1288.11075
Kritzer, Peter; Pillichshammer, Friedrich
2013
Dyadic diaphony of digital nets over $$\mathbb Z_2$$. Zbl 1130.11042
Dick, Josef; Pillichshammer, Friedrich
2005
The average distance between two points. Zbl 1183.52006
Burgstaller, Bernhard; Pillichshammer, Friedrich
2009
Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2017
Euler’s constant and averages of fractional parts. Zbl 1204.26005
Pillichshammer, Friedrich
2010
The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091
Pillichshammer, Friedrich; Pirsic, Gottlieb
2009
Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2007
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048
Dick, Josef; Pillichshammer, Friedrich
2014
Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015
Pillichshammer, Friedrich
2018
Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets. Zbl 1302.65012
Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2013
On the component by component construction of polynomial lattice point sets for numerical integration in weighted Sobolev spaces. Zbl 1338.11072
Kritzer, Peter; Pillichshammer, Friedrich
2011
On the discrepancy of the van der Corput sequence indexed by Fibonacci numbers. Zbl 1290.11111
Pillichshammer, Friedrich
2012
On the root mean square weighted $$L_{2}$$ discrepancy of scrambled nets. Zbl 1073.65005
Pillichshammer, Friedrich
2004
Weighted discrepancy and high-dimensional numerical integration. Zbl 1124.11314
Larcher, G.; Pillichshammer, F.; Scheicher, K.
2003
The weighted dyadic diaphony of digital sequences. Zbl 1228.11118
Kritzer, Peter; Pillichshammer, Friedrich
2008
The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009
Larcher, Gerhard; Pillichshammer, Friedrich
2008
A lower bound for the $$b$$-adic diaphony. Zbl 1140.11037
Cristea, Ligia L.; Pillichshammer, Friedrich
2007
Improvements of the discrepancy of the van der Corput sequence. Zbl 1119.11045
Kritzer, Peter; Pillichshammer, Friedrich
2005
Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061
Hofinger, Andreas; Pillichshammer, Friedrich
2009
Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 1456.11141
Neumüller, Mario; Pillichshammer, Friedrich
2018
Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration. Zbl 1428.11136
Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne
2017
Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050
Larcher, Gerhard; Pillichshammer, Friedrich
2014
Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002
Hellekalek, Peter; Kritzer, Peter; Pillichshammer, Friedrich
2016
Digital nets in dimension two with the optimal order of $$L_p$$ discrepancy. Zbl 1465.11171
Kritzinger, Ralph; Pillichshammer, Friedrich
2019
Secure pseudorandom bit generators and point sets with low star-discrepancy. Zbl 1469.11244
Gómez, Ana I.; Gómez-Pérez, Domingo; Pillichshammer, Friedrich
2021
Extreme and periodic $$L_2$$ discrepancy of plane point sets. Zbl 1483.11158
Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich
2021
A note on isotropic discrepancy and spectral test of lattice point sets. Zbl 1453.11099
Pillichshammer, Friedrich; Sonnleitner, Mathias
2020
A note on the periodic $$L_2$$-discrepancy of Korobov’s $$p$$-sets. Zbl 1448.11148
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich
2020
Discrepancy theory. Zbl 1454.11006
2020
On efficient weighted integration via a change of variables. Zbl 1451.65020
Kritzer, P.; Pillichshammer, F.; Plaskota, L.; Wasilkowski, G. W.
2020
Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals. Zbl 1469.65183
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2020
Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034
Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
2019
Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152
Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu
2019
Digital nets in dimension two with the optimal order of $$L_p$$ discrepancy. Zbl 1465.11171
Kritzinger, Ralph; Pillichshammer, Friedrich
2019
On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953
Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich
2018
Truncation dimension for function approximation. Zbl 1405.65021
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W.
2018
On Weyl products and uniform distribution modulo one. Zbl 1410.11106
Aistleitner, Christoph; Larcher, Gerhard; Pillichshammer, Friedrich; Eddin, Sumaia Saad; Tichy, Robert F.
2018
Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015
Pillichshammer, Friedrich
2018
Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 1456.11141
Neumüller, Mario; Pillichshammer, Friedrich
2018
Tractability of $$\mathbb{L}_2$$-approximation in hybrid function spaces. Zbl 1396.41014
Kritzer, Peter; Laimer, Helene; Pillichshammer, Friedrich
2018
Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices. Zbl 1385.65003
Dick, Josef; Pillichshammer, Friedrich; Suzuki, Kosuke; Ullrich, Mario; Yoshiki, Takehito
2018
A note on equivalence of anchored and ANOVA spaces; lower bounds. Zbl 1355.65027
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
2017
Optimal $$L_{p}$$-discrepancy bounds for second order digital sequences. Zbl 1394.11060
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2017
$$\mathbb{L}_\infty$$-approximation in Korobov spaces with exponential weights. Zbl 1367.41024
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2017
Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2017
Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration. Zbl 1428.11136
Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne
2017
Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2016
Approximation in Hermite spaces of smooth functions. Zbl 1338.65040
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2016
Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
2016
Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002
Hellekalek, Peter; Kritzer, Peter; Pillichshammer, Friedrich
2016
Tractability of multivariate integration in hybrid function spaces. Zbl 1356.65009
Kritzer, Peter; Pillichshammer, Friedrich
2016
Integration in Hermite spaces of analytic functions. Zbl 1316.65034
Irrgeher, Christian; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2015
From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063
Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich
2015
The weighted star discrepancy of Korobov’s $$p$$-sets. Zbl 1329.11078
Dick, Josef; Pillichshammer, Friedrich
2015
Optimal order of $$L_p$$-discrepancy of digit shifted Hammersley point sets in dimension 2. Zbl 1340.11062
Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich
2015
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich
2015
A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Zbl 1300.65004
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2015
$$L_p$$-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070
Kritzinger, Ralph; Pillichshammer, Friedrich
2015
Component-by-component construction of shifted Halton sequences. Zbl 1439.65032
Kritzer, Peter; Pillichshammer, Friedrich
2015
Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2015
Introduction to quasi-Monte Carlo integration and applications. Zbl 1309.65006
Leobacher, Gunther; Pillichshammer, Friedrich
2014
Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Approximation of analytic functions in Korobov spaces. Zbl 1342.41021
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich
2014
Tractability of multivariate analytic problems. Zbl 1333.65019
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
2014
Optimal $$\mathcal {L}_{2}$$ discrepancy bounds for higher order digital sequences over the finite field $$\mathbb {F}_{2}$$. Zbl 1294.11127
Dick, Josef; Pillichshammer, Friedrich
2014
Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086
Dick, Josef; Pillichshammer, Friedrich
2014
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
Dick, Josef; Pillichshammer, Friedrich
2014
A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086
Larcher, Gerhard; Pillichshammer, Friedrich
2014
Uniform distribution and quasi-Monte Carlo methods. Discrepancy, integration and applications. Based on invited talks of the workspop, Linz, Austria, October 14–18, 2013. Zbl 1291.11003
2014
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048
Dick, Josef; Pillichshammer, Friedrich
2014
Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050
Larcher, Gerhard; Pillichshammer, Friedrich
2014
Discrepancy estimates for index-transformed uniformly distributed sequences. Zbl 1368.11072
Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
2014
The $$p$$-adic diaphony of the Halton sequence. Zbl 1282.11087
Pillichshammer, Friedrich
2013
On the existence of low-diaphony sequences made of digital sequences and lattice point sets. Zbl 1288.11075
Kritzer, Peter; Pillichshammer, Friedrich
2013
Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets. Zbl 1302.65012
Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2013
A generalization of NUT digital $$(0,1)$$-sequences and best possible lower bounds for star discrepancy. Zbl 1286.11121
Faure, Henri; Pillichshammer, Friedrich
2013
Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules. Zbl 1244.65002
Baldeaux, Jan; Dick, Josef; Leobacher, Gunther; Nuyens, Dirk; Pillichshammer, Friedrich
2012
Polynomial lattice point sets. Zbl 1294.11129
Pillichshammer, Friedrich
2012
Low discrepancy polynomial lattice point sets. Zbl 1256.11042
Kritzer, Peter; Pillichshammer, Friedrich
2012
On the discrepancy of the van der Corput sequence indexed by Fibonacci numbers. Zbl 1290.11111
Pillichshammer, Friedrich
2012
Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077
Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk
2011
Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich
2011
Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2011
On the component by component construction of polynomial lattice point sets for numerical integration in weighted Sobolev spaces. Zbl 1338.11072
Kritzer, Peter; Pillichshammer, Friedrich
2011
A lower bound on a quantity related to the quality of polynomial lattices. Zbl 1247.11097
Kritzer, Peter; Pillichshammer, Friedrich
2011
$$L_2$$ discrepancy of linearly digit scrambled Zaremba point sets. Zbl 1333.11070
Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb
2011
$$L_2$$ discrepancy of generalized Zaremba point sets. Zbl 1277.11081
Faure, Henri; Pillichshammer, Friedrich
2011
Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012
Dick, Josef; Pillichshammer, Friedrich
2010
$$L_2$$ discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Zbl 1198.11072
Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb; Schmid, Wolfgang Ch.
2010
A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
2010
Euler’s constant and averages of fractional parts. Zbl 1204.26005
Pillichshammer, Friedrich
2010
Distribution properties of generalized van der Corput-Halton sequences and their subsequences. Zbl 1188.11038
Hofer, Roswitha; Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
2009
$$L_p$$ discrepancy of generalized two-dimensional Hammersley point sets. Zbl 1175.11042
Faure, Henri; Pillichshammer, Friedrich
2009
Construction algorithms for good extensible lattice rules. Zbl 1247.11100
Niederreiter, Harald; Pillichshammer, Friedrich
2009
$$L_2$$ discrepancy of two-dimensional digitally shifted Hammersley point sets in base $$b$$. Zbl 1228.11122
Faure, Henri; Pillichshammer, Friedrich
2009
Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088
Pillichshammer, Friedrich; Steinerberger, Stefan
2009
Distribution properties of sequences generated by $$Q$$-additive functions with respect to Cantor representation of integers. Zbl 1228.11114
Hofer, Roswitha; Pillichshammer, Friedrich; Pirsic, Gottlieb
2009
The average distance between two points. Zbl 1183.52006
Burgstaller, Bernhard; Pillichshammer, Friedrich
2009
The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091
Pillichshammer, Friedrich; Pirsic, Gottlieb
2009
Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061
Hofinger, Andreas; Pillichshammer, Friedrich
2009
Discrepancy of hyperplane nets and cyclic nets. Zbl 1184.65008
Pillichshammer, Friedrich; Pirsic, Gottlieb
2009
The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J.
2008
Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030
Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich
2008
Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006
Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich
2008
Tractability properties of the weighted star discrepancy. Zbl 1146.65002
Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch.
2008
The weighted dyadic diaphony of digital sequences. Zbl 1228.11118
Kritzer, Peter; Pillichshammer, Friedrich
2008
The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009
Larcher, Gerhard; Pillichshammer, Friedrich
2008
Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich
2007
A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Zbl 1150.11026
Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
2007
On the existence of higher order polynomial lattices based on a generalized figure of merit. Zbl 1130.65047
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Schmid, Wolfgang Ch.
2007
The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002
Cristea, Ligia L.; Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2007
Constructions of general polynomial lattices for multivariate integration. Zbl 1125.65006
Kritzer, Peter; Pillichshammer, Friedrich
2007
Uniform distribution of sequences connected with the weighted sum-of-digits function. Zbl 1201.11081
Pillichshammer, Friedrich
2007
Points sets with low $$L_p$$ discrepancy. Zbl 1153.11037
Kritzer, Peter; Pillichshammer, Friedrich
2007
The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J.
2007
A note on optimal point distributions in $$[0,1)^{s}$$. Zbl 1201.11084
Larcher, Gerhard; Pillichshammer, Friedrich
2007
Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2007
A lower bound for the $$b$$-adic diaphony. Zbl 1140.11037
Cristea, Ligia L.; Pillichshammer, Friedrich
2007
Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
2007
Dyadic diaphony of digital sequences. Zbl 1152.11036
Pillichshammer, Friedrich
2007
Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich
2006
An exact formula for $$L_2$$ discrepancy of the shifted Hammersley point set. Zbl 1147.11041
Kritzer, Peter; Pillichshammer, Friedrich
2006
Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich
2006
...and 29 more Documents
all top 5

### Cited by 398 Authors

 86 Pillichshammer, Friedrich 60 Dick, Josef 50 Kritzer, Peter 23 Kuo, Frances Y. 20 Hinrichs, Aicke 20 Nuyens, Dirk 19 Larcher, Gerhard 18 Goda, Takashi 17 Hofer, Roswitha 17 Sloan, Ian Hugh 15 Steinerberger, Stefan 13 Suzuki, Kosuke 13 Woźniakowski, Henryk 12 Wasilkowski, Grzegorz W. 12 Yoshiki, Takehito 11 Gnewuch, Michael 11 Kritzinger, Ralph 10 Leobacher, Gunther 9 Aistleitner, Christoph 9 Niederreiter, Harald 9 Ullrich, Mario 8 Owen, Art B. 8 Schwab, Christoph 8 Xu, Guiqiao 7 Faure, Henri 7 Markhasin, Lev 6 Baldeaux, Jan 6 Cools, Ronald 6 He, Zhijian 6 Hickernell, Fred J. 6 Irrgeher, Christian 6 Lemieux, Christiane 6 Leovey, Hernan 6 Ullrich, Tino 6 Wang, Xiaoqun 5 Brauchart, Johann S. 5 Ebert, Adrian 5 L’Ecuyer, Pierre 5 Liu, Yongping 5 Pausinger, Florian 5 Wang, Heping 4 Bilyk, Dmitry 4 Gerber, Mathieu 4 Hefter, Mario 4 Heitsch, Holger 4 Levin, Mordekhaĭ Borisovich 4 Matsumoto, Makoto 4 Oettershagen, Jens 4 Ritter, Klaus 4 Römisch, Werner 4 Suryanarayana, Gowri 4 Tichy, Robert Franz 4 Zhu, Houying 3 Basu, Kinjal 3 Brown, Louis 3 Harase, Shin 3 Le Gia, Quoc Thong 3 Lertchoosakul, Poj 3 Mhaskar, Hrushikesh N. 3 Nguyen, Dong T. P. 3 Nobile, Fabio 3 Oates, Chris J. 3 Ohori, Ryuichi 3 Papageorgiou, Anargyros 3 Petras, Iasonas 3 Rudolf, Daniel 3 Scheichl, Robert 3 Thonhauser, Stefan 2 Audet, Charles 2 Ben Abdellah, Amal 2 Bornn, Luke 2 Brandolini, Luca 2 Chen, Jia 2 Drmota, Michael 2 Dutkay, Dorin Ervin 2 Ehler, Martin 2 Esquivel, Hugo 2 Gantner, Robert Nicholas 2 Girolami, Mark A. 2 Gomez-Perez, Domingo 2 Gräf, Manuel 2 Graham, Ivan G. 2 Griebel, Michael 2 Griewank, Andreas 2 Hansen, Pierre 2 Hellekalek, Peter 2 Henrion, René 2 Hofer, Markus 2 Hofinger, Andreas 2 Iacò, Maria Rita 2 Jiménez Rugama, Lluís Antoni 2 Kaltenböck, Lisa 2 Kiderlen, Markus 2 Kühn, Thomas 2 Laimer, Helene 2 Lin, Guang 2 Messine, Frédéric 2 Migliorati, Giovanni 2 Nair, Radhakrishnan B. 2 Nichols, James A. ...and 298 more Authors
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### Cited in 121 Serials

 91 Journal of Complexity 21 Mathematics of Computation 18 Monatshefte für Mathematik 16 Journal of Approximation Theory 14 Journal of Computational and Applied Mathematics 14 SIAM Journal on Numerical Analysis 11 Numerische Mathematik 10 Foundations of Computational Mathematics 9 Journal of Number Theory 9 Finite Fields and their Applications 6 Discrete Mathematics 6 Mathematics and Computers in Simulation 6 Constructive Approximation 6 Numerical Algorithms 6 Indagationes Mathematicae. New Series 6 SIAM Journal on Scientific Computing 6 The Journal of Fourier Analysis and Applications 6 Statistics and Computing 5 Bulletin of the Australian Mathematical Society 5 Acta Arithmetica 5 Archiv der Mathematik 5 Proceedings of the American Mathematical Society 5 Journal de Théorie des Nombres de Bordeaux 4 Journal of Mathematical Analysis and Applications 4 The Annals of Statistics 4 Functiones et Approximatio. Commentarii Mathematici 4 Monte Carlo Methods and Applications 3 Advances in Mathematics 3 Mathematika 3 Journal of Global Optimization 3 European Journal of Operational Research 3 SIAM Review 3 Uniform Distribution Theory 3 SIAM/ASA Journal on Uncertainty Quantification 2 Computer Methods in Applied Mechanics and Engineering 2 Journal d’Analyse Mathématique 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Computing 2 Mathematische Nachrichten 2 Statistics & Probability Letters 2 Acta Applicandae Mathematicae 2 Statistical Science 2 The Annals of Applied Probability 2 Elemente der Mathematik 2 Stochastic Processes and their Applications 2 Mathematical Programming. Series A. Series B 2 Computational Optimization and Applications 2 Applied and Computational Harmonic Analysis 2 The ANZIAM Journal 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Science China. Mathematics 1 Advances in Applied Probability 1 Computers & Mathematics with Applications 1 Computer Physics Communications 1 Israel Journal of Mathematics 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Mathematical Notes 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Mathematische Semesterberichte 1 Periodica Mathematica Hungarica 1 Bulletin of Mathematical Biology 1 Theory of Probability and its Applications 1 Annales de l’Institut Fourier 1 Applied Mathematics and Computation 1 BIT 1 Information Sciences 1 Journal of Applied Probability 1 Journal of Optimization Theory and Applications 1 Journal für die Reine und Angewandte Mathematik 1 Journal of Statistical Planning and Inference 1 Manuscripta Mathematica 1 Mathematics of Operations Research 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Transactions of the American Mathematical Society 1 Acta Mathematica Hungarica 1 Applied Numerical Mathematics 1 Optimization 1 Probability Theory and Related Fields 1 Discrete & Computational Geometry 1 Journal of Scientific Computing 1 Annals of Operations Research 1 Computational Geometry 1 Designs, Codes and Cryptography 1 Bulletin of the American Mathematical Society. New Series 1 Computational Statistics and Data Analysis 1 Journal of Mathematical Imaging and Vision 1 Russian Mathematics 1 Advances in Computational Mathematics 1 Discrete and Continuous Dynamical Systems 1 Finance and Stochastics 1 Mathematical Methods of Operations Research 1 Journal of Inequalities and Applications 1 Journal of Applied Statistics 1 International Journal of Applied Mathematics and Computer Science 1 Computational Geosciences 1 CEJOR. Central European Journal of Operations Research 1 Methodology and Computing in Applied Probability 1 Scandinavian Actuarial Journal ...and 21 more Serials
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### Cited in 41 Fields

 278 Numerical analysis (65-XX) 196 Number theory (11-XX) 91 Approximations and expansions (41-XX) 45 Probability theory and stochastic processes (60-XX) 40 Statistics (62-XX) 34 Harmonic analysis on Euclidean spaces (42-XX) 33 Functional analysis (46-XX) 29 Computer science (68-XX) 17 Operations research, mathematical programming (90-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Partial differential equations (35-XX) 10 Combinatorics (05-XX) 10 Information and communication theory, circuits (94-XX) 7 Convex and discrete geometry (52-XX) 6 Operator theory (47-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 5 Real functions (26-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Differential geometry (53-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Measure and integration (28-XX) 3 Potential theory (31-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Geometry (51-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Biology and other natural sciences (92-XX) 3 Systems theory; control (93-XX) 2 Special functions (33-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Functions of a complex variable (30-XX) 1 Ordinary differential equations (34-XX) 1 Difference and functional equations (39-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral transforms, operational calculus (44-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Optics, electromagnetic theory (78-XX) 1 Geophysics (86-XX)

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