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Pillichshammer, Friedrich

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Author ID: pillichshammer.friedrich Recent zbMATH articles by "Pillichshammer, Friedrich"
Published as: Pillichshammer, F.; Pillichshammer, Friedrich
External Links: MGP · Wikidata · ORCID · GND
Documents Indexed: 144 Publications since 2000, including 5 Books
all top 5

Serials

18 Journal of Complexity
11 Uniform Distribution Theory
7 Acta Arithmetica
7 Monatshefte für Mathematik
5 Mathematics of Computation
5 Archiv der Mathematik
5 Finite Fields and their Applications
4 Bulletin of the Australian Mathematical Society
4 Functiones et Approximatio. Commentarii Mathematici
4 Journal of Approximation Theory
3 Journal of Computational and Applied Mathematics
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 Mathematics and Computers in Simulation
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

Publications by Year

Citations contained in zbMATH

118 Publications have been cited 977 times in 388 Documents Cited by Year
Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012
Dick, Josef; Pillichshammer, Friedrich
221
2010
Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021
Dick, Josef; Pillichshammer, Friedrich
42
2005
Introduction to quasi-Monte Carlo integration and applications. Zbl 1309.65006
Leobacher, Gunther; Pillichshammer, Friedrich
31
2014
Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007
Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H.
31
2005
Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
29
2014
Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077
Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk
26
2011
Approximation of analytic functions in Korobov spaces. Zbl 1342.41021
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
22
2014
The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J.
22
2008
Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich
21
2014
Integration in Hermite spaces of analytic functions. Zbl 1316.65034
Irrgeher, Christian; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
20
2015
Tractability of multivariate analytic problems. Zbl 1333.65019
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
19
2014
Distribution properties of generalized van der Corput-Halton sequences and their subsequences. Zbl 1188.11038
Hofer, Roswitha; Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
18
2009
Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich
18
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
15
2012
Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
14
2016
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
13
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
13
2005
Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086
Dick, Josef; Pillichshammer, Friedrich
12
2014
\(L_2\) discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Zbl 1198.11072
Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb; Schmid, Wolfgang Ch.
12
2010
Walsh series analysis of the \(L_2\)-discrepancy of symmetrized point sets. Zbl 1108.11309
Larcher, G.; Pillichshammer, F.
12
2001
Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich
11
2011
Precise distribution properties of the van der Corput sequence and related sequences. Zbl 1088.11060
Drmota, Michael; Larcher, Gerhard; Pillichshammer, Friedrich
11
2005
Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
11
2005
Sums of distances to the nearest integer and the discrepancy of digital nets. Zbl 1054.11039
Larcher, G.; Pillichshammer, F.
11
2003
Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
10
2016
Approximation in Hermite spaces of smooth functions. Zbl 1338.65040
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
10
2016
From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063
Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich
9
2015
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
Dick, Josef; Pillichshammer, Friedrich
9
2014
Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich
9
2006
On the discrepancy of \((0,1)\)-sequences. Zbl 1048.11061
Pillichshammer, Friedrich
9
2004
Bounds for the weighted \(L^p\) discrepancy and tractability of integration. Zbl 1366.11090
Leobacher, Gunther; Pillichshammer, Friedrich
8
2003
A note on equivalence of anchored and ANOVA spaces; lower bounds. Zbl 1355.65027
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
7
2017
An exact formula for \(L_2\) discrepancy of the shifted Hammersley point set. Zbl 1147.11041
Kritzer, Peter; Pillichshammer, Friedrich
7
2006
Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003
Dick, Josef; Pillichshammer, Friedrich
7
2005
On the \(L_p\)-discrepancy of the Hammersley point set. Zbl 1010.11043
Pillichshammer, Friedrich
7
2002
The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078
Dick, Josef; Pillichshammer, Friedrich
6
2015
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich
6
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
6
2015
Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
6
2011
\(L_p\) discrepancy of generalized two-dimensional Hammersley point sets. Zbl 1175.11042
Faure, Henri; Pillichshammer, Friedrich
6
2009
Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006
Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich
6
2008
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.
6
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
6
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
6
2007
On the sum of squared distances in the Euclidean plane. Zbl 0966.52007
Pillichshammer, Friedrich
6
2000
Optimal order of \(L_p\)-discrepancy of digit shifted Hammersley point sets in dimension 2. Zbl 1340.11062
Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich
5
2015
\(L_p\)-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070
Kritzinger, Ralph; Pillichshammer, Friedrich
5
2015
Polynomial lattice point sets. Zbl 1294.11129
Pillichshammer, Friedrich
5
2012
\(L_2\) discrepancy of two-dimensional digitally shifted Hammersley point sets in base \(b\). Zbl 1228.11122
Faure, Henri; Pillichshammer, Friedrich
5
2009
Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030
Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich
5
2008
Tractability properties of the weighted star discrepancy. Zbl 1146.65002
Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch.
5
2008
A note on the sum of distances under a diameter constraint. Zbl 1002.51015
Pillichshammer, Friedrich
5
2001
A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086
Larcher, Gerhard; Pillichshammer, Friedrich
4
2014
Low discrepancy polynomial lattice point sets. Zbl 1256.11042
Kritzer, Peter; Pillichshammer, Friedrich
4
2012
Construction algorithms for good extensible lattice rules. Zbl 1247.11100
Niederreiter, Harald; Pillichshammer, Friedrich
4
2009
Constructions of general polynomial lattices for multivariate integration. Zbl 1125.65006
Kritzer, Peter; Pillichshammer, Friedrich
4
2007
Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich
4
2006
Moments of the weighted sum-of-digits function. Zbl 1092.11007
Larcher, Gerhard; Pillichshammer, Friedrich
4
2005
On extremal point disributions in the Euclidean plane. Zbl 1026.52008
Pillichshammer, F.
4
2003
Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034
Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
3
2019
Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
3
2017
\(\mathbb{L}_\infty\)-approximation in Korobov spaces with exponential weights. Zbl 1367.41024
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
3
2017
The \(p\)-adic diaphony of the Halton sequence. Zbl 1282.11087
Pillichshammer, Friedrich
3
2013
On the existence of low-diaphony sequences made of digital sequences and lattice point sets. Zbl 1288.11075
Kritzer, Peter; Pillichshammer, Friedrich
3
2013
A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
3
2010
Euler’s constant and averages of fractional parts. Zbl 1204.26005
Pillichshammer, Friedrich
3
2010
Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088
Pillichshammer, Friedrich; Steinerberger, Stefan
3
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
3
2009
Uniform distribution of sequences connected with the weighted sum-of-digits function. Zbl 1201.11081
Pillichshammer, Friedrich
3
2007
A note on optimal point distributions in \([0,1)^{s}\). Zbl 1201.11084
Larcher, Gerhard; Pillichshammer, Friedrich
3
2007
The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J.
3
2007
Dyadic diaphony of digital nets over \(\mathbb Z_2\). Zbl 1130.11042
Dick, Josef; Pillichshammer, Friedrich
3
2005
Improved upper bounds for the star discrepancy of digital nets in dimension 3. Zbl 1054.11040
Pillichshammer, Friedrich
3
2003
Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152
Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu
2
2019
Truncation dimension for function approximation. Zbl 1405.65021
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W.
2
2018
Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
2
2017
Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002
Hellekalek, Peter; Kritzer, Peter; Pillichshammer, Friedrich
2
2016
Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050
Larcher, Gerhard; Pillichshammer, Friedrich
2
2014
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048
Dick, Josef; Pillichshammer, Friedrich
2
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
Kritzer, Peter (ed.); Niederreiter, Harald (ed.); Pillichshammer, Friedrich (ed.); Winterhof, Arne (ed.)
2
2014
Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets. Zbl 1302.65012
Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2
2013
On the discrepancy of the van der Corput sequence indexed by Fibonacci numbers. Zbl 1290.11111
Pillichshammer, Friedrich
2
2012
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
2
2011
Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061
Hofinger, Andreas; Pillichshammer, Friedrich
2
2009
The average distance between two points. Zbl 1183.52006
Burgstaller, Bernhard; Pillichshammer, Friedrich
2
2009
The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091
Pillichshammer, Friedrich; Pirsic, Gottlieb
2
2009
The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009
Larcher, Gerhard; Pillichshammer, Friedrich
2
2008
The weighted dyadic diaphony of digital sequences. Zbl 1228.11118
Kritzer, Peter; Pillichshammer, Friedrich
2
2008
Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2
2007
Points sets with low \(L_p\) discrepancy. Zbl 1153.11037
Kritzer, Peter; Pillichshammer, Friedrich
2
2007
Improvements of the discrepancy of the van der Corput sequence. Zbl 1119.11045
Kritzer, Peter; Pillichshammer, Friedrich
2
2005
On the root mean square weighted \(L_{2}\) discrepancy of scrambled nets. Zbl 1073.65005
Pillichshammer, Friedrich
2
2004
Weighted discrepancy and high-dimensional numerical integration. Zbl 1124.11314
Larcher, G.; Pillichshammer, F.; Scheicher, K.
2
2003
Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 07099381
Neumüller, Mario; Pillichshammer, Friedrich
1
2018
Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015
Pillichshammer, Friedrich
1
2018
On Weyl products and uniform distribution modulo one. Zbl 1410.11106
Aistleitner, Christoph; Larcher, Gerhard; Pillichshammer, Friedrich; Eddin, Sumaia Saad; Tichy, Robert F.
1
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
1
2017
Tractability of multivariate integration in hybrid function spaces. Zbl 1356.65009
Kritzer, Peter; Pillichshammer, Friedrich
1
2016
Component-by-component construction of shifted Halton sequences. Zbl 1439.65032
Kritzer, Peter; Pillichshammer, Friedrich
1
2015
Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
1
2015
Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034
Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
3
2019
Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152
Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu
2
2019
Truncation dimension for function approximation. Zbl 1405.65021
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W.
2
2018
Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 07099381
Neumüller, Mario; Pillichshammer, Friedrich
1
2018
Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015
Pillichshammer, Friedrich
1
2018
On Weyl products and uniform distribution modulo one. Zbl 1410.11106
Aistleitner, Christoph; Larcher, Gerhard; Pillichshammer, Friedrich; Eddin, Sumaia Saad; Tichy, Robert F.
1
2018
A note on equivalence of anchored and ANOVA spaces; lower bounds. Zbl 1355.65027
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
7
2017
Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060
Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich
3
2017
\(\mathbb{L}_\infty\)-approximation in Korobov spaces with exponential weights. Zbl 1367.41024
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
3
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
2
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
1
2017
Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
14
2016
Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098
Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W.
10
2016
Approximation in Hermite spaces of smooth functions. Zbl 1338.65040
Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
10
2016
Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002
Hellekalek, Peter; Kritzer, Peter; Pillichshammer, Friedrich
2
2016
Tractability of multivariate integration in hybrid function spaces. Zbl 1356.65009
Kritzer, Peter; Pillichshammer, Friedrich
1
2016
Integration in Hermite spaces of analytic functions. Zbl 1316.65034
Irrgeher, Christian; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
20
2015
From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063
Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich
9
2015
The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078
Dick, Josef; Pillichshammer, Friedrich
6
2015
Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002
Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich
6
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
6
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
5
2015
\(L_p\)-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070
Kritzinger, Ralph; Pillichshammer, Friedrich
5
2015
Component-by-component construction of shifted Halton sequences. Zbl 1439.65032
Kritzer, Peter; Pillichshammer, Friedrich
1
2015
Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
1
2015
Introduction to quasi-Monte Carlo integration and applications. Zbl 1309.65006
Leobacher, Gunther; Pillichshammer, Friedrich
31
2014
Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
29
2014
Approximation of analytic functions in Korobov spaces. Zbl 1342.41021
Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
22
2014
Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070
Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich
21
2014
Tractability of multivariate analytic problems. Zbl 1333.65019
Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk
19
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
13
2014
Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086
Dick, Josef; Pillichshammer, Friedrich
12
2014
Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061
Dick, Josef; Pillichshammer, Friedrich
9
2014
A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086
Larcher, Gerhard; Pillichshammer, Friedrich
4
2014
Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050
Larcher, Gerhard; Pillichshammer, Friedrich
2
2014
The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048
Dick, Josef; Pillichshammer, Friedrich
2
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
Kritzer, Peter (ed.); Niederreiter, Harald (ed.); Pillichshammer, Friedrich (ed.); Winterhof, Arne (ed.)
2
2014
Discrepancy estimates for index-transformed uniformly distributed sequences. Zbl 1368.11072
Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
1
2014
The \(p\)-adic diaphony of the Halton sequence. Zbl 1282.11087
Pillichshammer, Friedrich
3
2013
On the existence of low-diaphony sequences made of digital sequences and lattice point sets. Zbl 1288.11075
Kritzer, Peter; Pillichshammer, Friedrich
3
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
2
2013
A generalization of NUT digital \((0,1)\)-sequences and best possible lower bounds for star discrepancy. Zbl 1286.11121
Faure, Henri; Pillichshammer, Friedrich
1
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
15
2012
Polynomial lattice point sets. Zbl 1294.11129
Pillichshammer, Friedrich
5
2012
Low discrepancy polynomial lattice point sets. Zbl 1256.11042
Kritzer, Peter; Pillichshammer, Friedrich
4
2012
On the discrepancy of the van der Corput sequence indexed by Fibonacci numbers. Zbl 1290.11111
Pillichshammer, Friedrich
2
2012
Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077
Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk
26
2011
Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003
Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich
11
2011
Duality theory and propagation rules for higher order nets. Zbl 1229.11103
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
6
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
2
2011
\(L_2\) discrepancy of generalized Zaremba point sets. Zbl 1277.11081
Faure, Henri; Pillichshammer, Friedrich
1
2011
\(L_2\) discrepancy of linearly digit scrambled Zaremba point sets. Zbl 1333.11070
Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb
1
2011
A lower bound on a quantity related to the quality of polynomial lattices. Zbl 1247.11097
Kritzer, Peter; Pillichshammer, Friedrich
1
2011
Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012
Dick, Josef; Pillichshammer, Friedrich
221
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.
12
2010
A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071
Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich
3
2010
Euler’s constant and averages of fractional parts. Zbl 1204.26005
Pillichshammer, Friedrich
3
2010
Distribution properties of generalized van der Corput-Halton sequences and their subsequences. Zbl 1188.11038
Hofer, Roswitha; Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich
18
2009
\(L_p\) discrepancy of generalized two-dimensional Hammersley point sets. Zbl 1175.11042
Faure, Henri; Pillichshammer, Friedrich
6
2009
\(L_2\) discrepancy of two-dimensional digitally shifted Hammersley point sets in base \(b\). Zbl 1228.11122
Faure, Henri; Pillichshammer, Friedrich
5
2009
Construction algorithms for good extensible lattice rules. Zbl 1247.11100
Niederreiter, Harald; Pillichshammer, Friedrich
4
2009
Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088
Pillichshammer, Friedrich; Steinerberger, Stefan
3
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
3
2009
Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061
Hofinger, Andreas; Pillichshammer, Friedrich
2
2009
The average distance between two points. Zbl 1183.52006
Burgstaller, Bernhard; Pillichshammer, Friedrich
2
2009
The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091
Pillichshammer, Friedrich; Pirsic, Gottlieb
2
2009
Discrepancy of hyperplane nets and cyclic nets. Zbl 1184.65008
Pillichshammer, Friedrich; Pirsic, Gottlieb
1
2009
The construction of good extensible rank-1 lattices. Zbl 1211.11092
Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J.
22
2008
Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006
Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich
6
2008
Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030
Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich
5
2008
Tractability properties of the weighted star discrepancy. Zbl 1146.65002
Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch.
5
2008
The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009
Larcher, Gerhard; Pillichshammer, Friedrich
2
2008
The weighted dyadic diaphony of digital sequences. Zbl 1228.11118
Kritzer, Peter; Pillichshammer, Friedrich
2
2008
Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005
Dick, Josef; Pillichshammer, Friedrich
18
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.
6
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
6
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
6
2007
Constructions of general polynomial lattices for multivariate integration. Zbl 1125.65006
Kritzer, Peter; Pillichshammer, Friedrich
4
2007
Uniform distribution of sequences connected with the weighted sum-of-digits function. Zbl 1201.11081
Pillichshammer, Friedrich
3
2007
A note on optimal point distributions in \([0,1)^{s}\). Zbl 1201.11084
Larcher, Gerhard; Pillichshammer, Friedrich
3
2007
The construction of good extensible Korobov rules. Zbl 1131.11051
Dick, J.; Pillichshammer, F.; Waterhouse, B. J.
3
2007
Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039
Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich
2
2007
Points sets with low \(L_p\) discrepancy. Zbl 1153.11037
Kritzer, Peter; Pillichshammer, Friedrich
2
2007
Dyadic diaphony of digital sequences. Zbl 1152.11036
Pillichshammer, Friedrich
1
2007
A lower bound for the \(b\)-adic diaphony. Zbl 1140.11037
Cristea, Ligia L.; Pillichshammer, Friedrich
1
2007
Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
1
2007
Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023
Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich
9
2006
An exact formula for \(L_2\) discrepancy of the shifted Hammersley point set. Zbl 1147.11041
Kritzer, Peter; Pillichshammer, Friedrich
7
2006
Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025
Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich
4
2006
An extremum problem for convex polygons. Zbl 1165.51008
Larcher, Gerhard; Pillichshammer, Friedrich
1
2006
Digital sequences with best possible order of \(L_2\)-discrepancy. Zbl 1121.11049
Pillichshammer, Friedrich
1
2006
Periodic functions with bounded remainder. Zbl 1115.11044
Dick, Josef; Pillichshammer, Friedrich
1
2006
On the mean square weighted \(\mathcal {L}_2\) discrepancy of randomized digital nets in prime base. Zbl 1142.11345
Cristea, Ligia L.; Dick, Josef; Pillichshammer, Friedrich
1
2006
Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021
Dick, Josef; Pillichshammer, Friedrich
42
2005
Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007
Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H.
31
2005
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
13
2005
Precise distribution properties of the van der Corput sequence and related sequences. Zbl 1088.11060
Drmota, Michael; Larcher, Gerhard; Pillichshammer, Friedrich
11
2005
Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040
Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich
11
2005
Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003
Dick, Josef; Pillichshammer, Friedrich
7
2005
Moments of the weighted sum-of-digits function. Zbl 1092.11007
Larcher, Gerhard; Pillichshammer, Friedrich
4
2005
...and 18 more Documents
all top 5

Cited by 331 Authors

75 Pillichshammer, Friedrich
57 Dick, Josef
45 Kritzer, Peter
19 Kuo, Frances Y.
19 Larcher, Gerhard
18 Goda, Takashi
18 Hinrichs, Aicke
15 Hofer, Roswitha
14 Nuyens, Dirk
14 Sloan, Ian Hugh
13 Suzuki, Kosuke
12 Steinerberger, Stefan
12 Woźniakowski, Henryk
12 Yoshiki, Takehito
10 Aistleitner, Christoph
10 Gnewuch, Michael
10 Leobacher, Gunther
10 Wasilkowski, Grzegorz W.
9 Niederreiter, Harald
8 Schwab, Christoph
8 Ullrich, Mario
8 Xu, Guiqiao
7 Hickernell, Fred J.
7 Kritzinger, Ralph
7 Markhasin, Lev
6 Baldeaux, Jan
6 Brauchart, Johann S.
6 Faure, Henri
6 Leovey, Hernan
6 Owen, Art B.
5 Irrgeher, Christian
5 Liu, Yongping
5 Pausinger, Florian
5 Wang, Xiaoqun
4 Bilyk, Dmitry
4 Cools, Ronald
4 He, Zhijian
4 Heitsch, Holger
4 Lemieux, Christiane
4 Matsumoto, Makoto
4 Suryanarayana, Gowri
4 Tichy, Robert Franz
4 Ullrich, Tino
4 Wang, Heping
4 Zhu, Houying
3 Basu, Kinjal
3 Gerber, Mathieu
3 Harase, Shin
3 Hefter, Mario
3 Le Gia, Quoc Thong
3 L’Ecuyer, Pierre
3 Lertchoosakul, Poj
3 Levin, Mordekhaĭ Borisovich
3 Oettershagen, Jens
3 Ohori, Ryuichi
3 Papageorgiou, Anargyros
3 Petras, Iasonas
3 Ritter, Klaus
3 Römisch, Werner
3 Rudolf, Daniel
3 Scheichl, Robert
3 Thonhauser, Stefan
2 Ammon, A.
2 Audet, Charles
2 Bornn, Luke
2 Chen, Jia
2 Cristea, Ligia-Loreta
2 Doerr, Benjamin
2 Drmota, Michael
2 Dutkay, Dorin Ervin
2 Ebert, Adrian
2 Ehler, Martin
2 Gantner, Robert Nicholas
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 Jansen, Karl
2 Jiménez Rugama, Lluís Antoni
2 Laimer, Helene
2 Messine, Frédéric
2 Mhaskar, Hrushikesh N.
2 Nair, Radhakrishnan B.
2 Nichols, James A.
2 Nobile, Fabio
2 Novak, Erich
2 Oates, Chris J.
2 Picioroaga, Gabriel
2 Pirsic, Isabel
2 Schmid, Wolfgang Ch.
2 Seri, Raffaello
2 Temirgaliev, Nurlan Temirgalievich
2 Tezuka, Shu
2 Waterhouse, Benjamin J.
...and 231 more Authors
all top 5

Cited in 107 Serials

82 Journal of Complexity
17 Mathematics of Computation
17 Journal of Approximation Theory
14 Monatshefte für Mathematik
13 SIAM Journal on Numerical Analysis
11 Journal of Computational and Applied Mathematics
9 Numerische Mathematik
9 Finite Fields and their Applications
8 Journal of Number Theory
8 Foundations of Computational Mathematics
6 Discrete Mathematics
6 Constructive Approximation
6 Numerical Algorithms
6 Indagationes Mathematicae. New Series
6 Statistics and Computing
5 Bulletin of the Australian Mathematical Society
5 SIAM Journal on Scientific Computing
5 Journal de Théorie des Nombres de Bordeaux
4 Archiv der Mathematik
4 Functiones et Approximatio. Commentarii Mathematici
4 Proceedings of the American Mathematical Society
4 The Journal of Fourier Analysis and Applications
3 Journal of Mathematical Analysis and Applications
3 Acta Arithmetica
3 Mathematika
3 Journal of Global Optimization
3 Monte Carlo Methods and Applications
2 Computer Physics Communications
2 Journal d’Analyse Mathématique
2 The Annals of Statistics
2 Computing
2 Journal of Statistical Planning and Inference
2 Mathematische Nachrichten
2 Statistics & Probability Letters
2 Acta Applicandae Mathematicae
2 Statistical Science
2 Elemente der Mathematik
2 European Journal of Operational Research
2 SIAM Review
2 Stochastic Processes and their Applications
2 Computational Optimization and Applications
2 Applied and Computational Harmonic Analysis
2 The ANZIAM Journal
1 Advances in Applied Probability
1 Computers & Mathematics with Applications
1 Computer Methods in Applied Mechanics and Engineering
1 Discrete Applied Mathematics
1 Israel Journal of Mathematics
1 Journal of Statistical Physics
1 Mathematical Notes
1 Periodica Mathematica Hungarica
1 Physics Letters. A
1 Advances in Mathematics
1 Annales de l’Institut Fourier
1 Annali di Matematica Pura ed Applicata. Serie Quarta
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 Manuscripta Mathematica
1 Mathematics and Computers in Simulation
1 Mathematics of Operations Research
1 Mathematica Slovaca
1 Mathematische Zeitschrift
1 Acta Mathematica Hungarica
1 Applied Numerical Mathematics
1 Optimization
1 Probability Theory and Related Fields
1 Discrete & Computational Geometry
1 Annals of Operations Research
1 The Annals of Applied Probability
1 Computational Geometry
1 Designs, Codes and Cryptography
1 Bulletin of the American Mathematical Society. New Series
1 Mathematical Programming. Series A. Series B
1 Journal of Mathematical Imaging and Vision
1 Russian Mathematics
1 Advances in Computational Mathematics
1 Finance and Stochastics
1 Mathematical Methods of Operations Research
1 Journal of Inequalities and Applications
1 Journal of Applied Statistics
1 Computational Geosciences
1 CEJOR. Central European Journal of Operations Research
1 Methodology and Computing in Applied Probability
1 Scandinavian Actuarial Journal
1 Quantitative Finance
1 Archives of Computational Methods in Engineering
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Quantum Information Processing
1 International Journal of Wavelets, Multiresolution and Information Processing
1 Computational Management Science
1 Advances in Difference Equations
1 International Journal of Number Theory
1 Chebyshevskiĭ Sbornik
1 Proceedings of the Steklov Institute of Mathematics
1 Electronic Journal of Statistics
1 Probability Surveys
...and 7 more Serials

Citations by Year

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