Edit Profile (opens in new tab) Pillichshammer, Friedrich Compute Distance To: Compute 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 all top 5 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) Publications by Year all cited Publications top 5 cited Publications 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 1282.65012Dick, Josef; Pillichshammer, Friedrich 246 2010 Introduction to quasi-Monte Carlo integration and applications. Zbl 1309.65006Leobacher, Gunther; Pillichshammer, Friedrich 48 2014 Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021Dick, Josef; Pillichshammer, Friedrich 45 2005 Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H. 35 2005 Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk 32 2011 Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 31 2014 Approximation of analytic functions in Korobov spaces. Zbl 1342.41021Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 28 2014 Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich 25 2014 Integration in Hermite spaces of analytic functions. Zbl 1316.65034Irrgeher, Christian; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 25 2015 The construction of good extensible rank-1 lattices. Zbl 1211.11092Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J. 21 2008 Tractability of multivariate analytic problems. Zbl 1333.65019Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 20 2014 Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 20 2016 Distribution properties of generalized van der Corput-Halton sequences and their subsequences. Zbl 1188.11038Hofer, 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 1130.65005Dick, 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 1244.65002Baldeaux, Jan; Dick, Josef; Leobacher, Gunther; Nuyens, Dirk; Pillichshammer, Friedrich 17 2012 Optimal \(\mathcal {L}_{2}\) discrepancy bounds for higher order digital sequences over the finite field \(\mathbb {F}_{2}\). Zbl 1294.11127Dick, Josef; Pillichshammer, Friedrich 16 2014 On the mean square weighted \({\mathcal L}_2\) discrepancy of randomized digital \((t,m,s)\)-nets over \({\mathbb Z}_2\). Zbl 1080.11058Dick, Josef; Pillichshammer, Friedrich 16 2005 Approximation in Hermite spaces of smooth functions. Zbl 1338.65040Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 15 2016 \(L_2\) discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Zbl 1198.11072Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb; Schmid, Wolfgang Ch. 13 2010 Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086Dick, Josef; Pillichshammer, Friedrich 13 2014 Sums of distances to the nearest integer and the discrepancy of digital nets. Zbl 1054.11039Larcher, G.; Pillichshammer, F. 13 2003 Walsh series analysis of the \(L_2\)-discrepancy of symmetrized point sets. Zbl 1108.11309Larcher, G.; Pillichshammer, F. 13 2001 Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 13 2005 Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061Dick, Josef; Pillichshammer, Friedrich 13 2014 Precise distribution properties of the van der Corput sequence and related sequences. Zbl 1088.11060Drmota, Michael; Larcher, Gerhard; Pillichshammer, Friedrich 12 2005 From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich 12 2015 Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 12 2016 Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich 11 2011 On the discrepancy of \((0,1)\)-sequences. Zbl 1048.11061Pillichshammer, Friedrich 11 2004 On the \(L_p\)-discrepancy of the Hammersley point set. Zbl 1010.11043Pillichshammer, Friedrich 9 2002 Bounds for the weighted \(L^p\) discrepancy and tractability of integration. Zbl 1366.11090Leobacher, Gunther; Pillichshammer, Friedrich 9 2003 Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich 9 2006 The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078Dick, Josef; Pillichshammer, Friedrich 9 2015 An exact formula for \(L_2\) discrepancy of the shifted Hammersley point set. Zbl 1147.11041Kritzer, Peter; Pillichshammer, Friedrich 8 2006 A note on equivalence of anchored and ANOVA spaces; lower bounds. Zbl 1355.65027Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 8 2017 Optimal order of \(L_p\)-discrepancy of digit shifted Hammersley point sets in dimension 2. Zbl 1340.11062Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich 8 2015 Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich 8 2015 A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Zbl 1150.11026Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich 7 2007 A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Zbl 1300.65004Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 7 2015 Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003Dick, Josef; Pillichshammer, Friedrich 7 2005 \(L_p\) discrepancy of generalized two-dimensional Hammersley point sets. Zbl 1175.11042Faure, Henri; Pillichshammer, Friedrich 7 2009 Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich 7 2008 Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich 7 2008 \(L_p\)-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070Kritzinger, Ralph; Pillichshammer, Friedrich 7 2015 On the sum of squared distances in the Euclidean plane. Zbl 0966.52007Pillichshammer, Friedrich 6 2000 On the existence of higher order polynomial lattices based on a generalized figure of merit. Zbl 1130.65047Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 6 2007 Duality theory and propagation rules for higher order nets. Zbl 1229.11103Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 6 2011 Tractability properties of the weighted star discrepancy. Zbl 1146.65002Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 6 2008 The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002Cristea, Ligia L.; Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 6 2007 A note on the sum of distances under a diameter constraint. Zbl 1002.51015Pillichshammer, Friedrich 5 2001 Polynomial lattice point sets. Zbl 1294.11129Pillichshammer, Friedrich 5 2012 Construction algorithms for good extensible lattice rules. Zbl 1247.11100Niederreiter, Harald; Pillichshammer, Friedrich 5 2009 \(L_2\) discrepancy of two-dimensional digitally shifted Hammersley point sets in base \(b\). Zbl 1228.11122Faure, Henri; Pillichshammer, Friedrich 5 2009 Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 5 2017 \(\mathbb{L}_\infty\)-approximation in Korobov spaces with exponential weights. Zbl 1367.41024Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 5 2017 Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 5 2019 Constructions of general polynomial lattices for multivariate integration. Zbl 1125.65006Kritzer, Peter; Pillichshammer, Friedrich 4 2007 Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088Pillichshammer, Friedrich; Steinerberger, Stefan 4 2009 On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich 4 2018 Low discrepancy polynomial lattice point sets. Zbl 1256.11042Kritzer, Peter; Pillichshammer, Friedrich 4 2012 Moments of the weighted sum-of-digits function. Zbl 1092.11007Larcher, Gerhard; Pillichshammer, Friedrich 4 2005 Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich 4 2006 Uniform distribution of sequences connected with the weighted sum-of-digits function. Zbl 1201.11081Pillichshammer, Friedrich 4 2007 On extremal point disributions in the Euclidean plane. Zbl 1026.52008Pillichshammer, F. 4 2003 Points sets with low \(L_p\) discrepancy. Zbl 1153.11037Kritzer, Peter; Pillichshammer, Friedrich 3 2007 The construction of good extensible Korobov rules. Zbl 1131.11051Dick, J.; Pillichshammer, F.; Waterhouse, B. J. 3 2007 A note on optimal point distributions in \([0,1)^{s}\). Zbl 1201.11084Larcher, Gerhard; Pillichshammer, Friedrich 3 2007 Distribution properties of sequences generated by \(Q\)-additive functions with respect to Cantor representation of integers. Zbl 1228.11114Hofer, Roswitha; Pillichshammer, Friedrich; Pirsic, Gottlieb 3 2009 A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086Larcher, Gerhard; Pillichshammer, Friedrich 3 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 3 2014 Truncation dimension for function approximation. Zbl 1405.65021Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W. 3 2018 Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu 3 2019 On Weyl products and uniform distribution modulo one. Zbl 1410.11106Aistleitner, Christoph; Larcher, Gerhard; Pillichshammer, Friedrich; Eddin, Sumaia Saad; Tichy, Robert F. 3 2018 Improved upper bounds for the star discrepancy of digital nets in dimension 3. Zbl 1054.11040Pillichshammer, Friedrich 3 2003 A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 3 2010 The \(p\)-adic diaphony of the Halton sequence. Zbl 1282.11087Pillichshammer, Friedrich 3 2013 On the existence of low-diaphony sequences made of digital sequences and lattice point sets. Zbl 1288.11075Kritzer, Peter; Pillichshammer, Friedrich 3 2013 Dyadic diaphony of digital nets over \(\mathbb Z_2\). Zbl 1130.11042Dick, Josef; Pillichshammer, Friedrich 3 2005 The average distance between two points. Zbl 1183.52006Burgstaller, Bernhard; Pillichshammer, Friedrich 3 2009 Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 3 2017 Euler’s constant and averages of fractional parts. Zbl 1204.26005Pillichshammer, Friedrich 3 2010 The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091Pillichshammer, Friedrich; Pirsic, Gottlieb 2 2009 Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 2 2007 The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048Dick, Josef; Pillichshammer, Friedrich 2 2014 Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015Pillichshammer, Friedrich 2 2018 Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets. Zbl 1302.65012Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 2 2013 On the component by component construction of polynomial lattice point sets for numerical integration in weighted Sobolev spaces. Zbl 1338.11072Kritzer, Peter; Pillichshammer, Friedrich 2 2011 On the discrepancy of the van der Corput sequence indexed by Fibonacci numbers. Zbl 1290.11111Pillichshammer, Friedrich 2 2012 On the root mean square weighted \(L_{2}\) discrepancy of scrambled nets. Zbl 1073.65005Pillichshammer, Friedrich 2 2004 Weighted discrepancy and high-dimensional numerical integration. Zbl 1124.11314Larcher, G.; Pillichshammer, F.; Scheicher, K. 2 2003 The weighted dyadic diaphony of digital sequences. Zbl 1228.11118Kritzer, Peter; Pillichshammer, Friedrich 2 2008 The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009Larcher, Gerhard; Pillichshammer, Friedrich 2 2008 A lower bound for the \(b\)-adic diaphony. Zbl 1140.11037Cristea, Ligia L.; Pillichshammer, Friedrich 2 2007 Improvements of the discrepancy of the van der Corput sequence. Zbl 1119.11045Kritzer, Peter; Pillichshammer, Friedrich 2 2005 Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061Hofinger, Andreas; Pillichshammer, Friedrich 2 2009 Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 1456.11141Neumüller, Mario; Pillichshammer, Friedrich 2 2018 Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration. Zbl 1428.11136Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne 2 2017 Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050Larcher, Gerhard; Pillichshammer, Friedrich 2 2014 Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002Hellekalek, Peter; Kritzer, Peter; Pillichshammer, Friedrich 2 2016 Digital nets in dimension two with the optimal order of \(L_p\) discrepancy. Zbl 1465.11171Kritzinger, Ralph; Pillichshammer, Friedrich 2 2019 Secure pseudorandom bit generators and point sets with low star-discrepancy. Zbl 1469.11244Gómez, Ana I.; Gómez-Pérez, Domingo; Pillichshammer, Friedrich 1 2021 Extreme and periodic \(L_2\) discrepancy of plane point sets. Zbl 1483.11158Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich 1 2021 A note on isotropic discrepancy and spectral test of lattice point sets. Zbl 1453.11099Pillichshammer, Friedrich; Sonnleitner, Mathias 1 2020 A note on the periodic \(L_2\)-discrepancy of Korobov’s \(p\)-sets. Zbl 1448.11148Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich 1 2020 Discrepancy theory. Zbl 1454.11006 1 2020 On efficient weighted integration via a change of variables. Zbl 1451.65020Kritzer, P.; Pillichshammer, F.; Plaskota, L.; Wasilkowski, G. W. 1 2020 Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals. Zbl 1469.65183Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 1 2020 Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 5 2019 Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu 3 2019 Digital nets in dimension two with the optimal order of \(L_p\) discrepancy. Zbl 1465.11171Kritzinger, Ralph; Pillichshammer, Friedrich 2 2019 On the optimal order of integration in Hermite spaces with finite smoothness. Zbl 06862953Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich 4 2018 Truncation dimension for function approximation. Zbl 1405.65021Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W. 3 2018 On Weyl products and uniform distribution modulo one. Zbl 1410.11106Aistleitner, Christoph; Larcher, Gerhard; Pillichshammer, Friedrich; Eddin, Sumaia Saad; Tichy, Robert F. 3 2018 Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015Pillichshammer, Friedrich 2 2018 Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 1456.11141Neumüller, Mario; Pillichshammer, Friedrich 2 2018 Tractability of \(\mathbb{L}_2\)-approximation in hybrid function spaces. Zbl 1396.41014Kritzer, Peter; Laimer, Helene; Pillichshammer, Friedrich 1 2018 Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices. Zbl 1385.65003Dick, Josef; Pillichshammer, Friedrich; Suzuki, Kosuke; Ullrich, Mario; Yoshiki, Takehito 1 2018 A note on equivalence of anchored and ANOVA spaces; lower bounds. Zbl 1355.65027Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 8 2017 Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 5 2017 \(\mathbb{L}_\infty\)-approximation in Korobov spaces with exponential weights. Zbl 1367.41024Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 5 2017 Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 3 2017 Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration. Zbl 1428.11136Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne 2 2017 Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 20 2016 Approximation in Hermite spaces of smooth functions. Zbl 1338.65040Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 15 2016 Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 12 2016 Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002Hellekalek, Peter; Kritzer, Peter; Pillichshammer, Friedrich 2 2016 Tractability of multivariate integration in hybrid function spaces. Zbl 1356.65009Kritzer, Peter; Pillichshammer, Friedrich 1 2016 Integration in Hermite spaces of analytic functions. Zbl 1316.65034Irrgeher, Christian; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 25 2015 From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich 12 2015 The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078Dick, Josef; Pillichshammer, Friedrich 9 2015 Optimal order of \(L_p\)-discrepancy of digit shifted Hammersley point sets in dimension 2. Zbl 1340.11062Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich 8 2015 Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002Dick, Josef; Hinrichs, Aicke; Pillichshammer, Friedrich 8 2015 A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Zbl 1300.65004Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 7 2015 \(L_p\)-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070Kritzinger, Ralph; Pillichshammer, Friedrich 7 2015 Component-by-component construction of shifted Halton sequences. Zbl 1439.65032Kritzer, Peter; Pillichshammer, Friedrich 1 2015 Numerical integration in log-Korobov and log-cosine spaces. Zbl 1339.65008Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 1 2015 Introduction to quasi-Monte Carlo integration and applications. Zbl 1309.65006Leobacher, Gunther; Pillichshammer, Friedrich 48 2014 Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 31 2014 Approximation of analytic functions in Korobov spaces. Zbl 1342.41021Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 28 2014 Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich 25 2014 Tractability of multivariate analytic problems. Zbl 1333.65019Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 20 2014 Optimal \(\mathcal {L}_{2}\) discrepancy bounds for higher order digital sequences over the finite field \(\mathbb {F}_{2}\). Zbl 1294.11127Dick, Josef; Pillichshammer, Friedrich 16 2014 Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086Dick, Josef; Pillichshammer, Friedrich 13 2014 Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061Dick, Josef; Pillichshammer, Friedrich 13 2014 A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086Larcher, Gerhard; Pillichshammer, Friedrich 3 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 3 2014 The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048Dick, Josef; Pillichshammer, Friedrich 2 2014 Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050Larcher, Gerhard; Pillichshammer, Friedrich 2 2014 Discrepancy estimates for index-transformed uniformly distributed sequences. Zbl 1368.11072Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich 1 2014 The \(p\)-adic diaphony of the Halton sequence. Zbl 1282.11087Pillichshammer, Friedrich 3 2013 On the existence of low-diaphony sequences made of digital sequences and lattice point sets. Zbl 1288.11075Kritzer, Peter; Pillichshammer, Friedrich 3 2013 Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets. Zbl 1302.65012Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 2 2013 A generalization of NUT digital \((0,1)\)-sequences and best possible lower bounds for star discrepancy. Zbl 1286.11121Faure, 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 1244.65002Baldeaux, Jan; Dick, Josef; Leobacher, Gunther; Nuyens, Dirk; Pillichshammer, Friedrich 17 2012 Polynomial lattice point sets. Zbl 1294.11129Pillichshammer, Friedrich 5 2012 Low discrepancy polynomial lattice point sets. Zbl 1256.11042Kritzer, Peter; Pillichshammer, Friedrich 4 2012 On the discrepancy of the van der Corput sequence indexed by Fibonacci numbers. Zbl 1290.11111Pillichshammer, Friedrich 2 2012 Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk 32 2011 Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich 11 2011 Duality theory and propagation rules for higher order nets. Zbl 1229.11103Baldeaux, 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 1338.11072Kritzer, Peter; Pillichshammer, Friedrich 2 2011 A lower bound on a quantity related to the quality of polynomial lattices. Zbl 1247.11097Kritzer, Peter; Pillichshammer, Friedrich 1 2011 \(L_2\) discrepancy of linearly digit scrambled Zaremba point sets. Zbl 1333.11070Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb 1 2011 \(L_2\) discrepancy of generalized Zaremba point sets. Zbl 1277.11081Faure, Henri; Pillichshammer, Friedrich 1 2011 Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012Dick, Josef; Pillichshammer, Friedrich 246 2010 \(L_2\) discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Zbl 1198.11072Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb; Schmid, Wolfgang Ch. 13 2010 A characterization of higher order nets using Weyl sums and its applications. Zbl 1249.11071Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 3 2010 Euler’s constant and averages of fractional parts. Zbl 1204.26005Pillichshammer, Friedrich 3 2010 Distribution properties of generalized van der Corput-Halton sequences and their subsequences. Zbl 1188.11038Hofer, Roswitha; Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich 18 2009 \(L_p\) discrepancy of generalized two-dimensional Hammersley point sets. Zbl 1175.11042Faure, Henri; Pillichshammer, Friedrich 7 2009 Construction algorithms for good extensible lattice rules. Zbl 1247.11100Niederreiter, Harald; Pillichshammer, Friedrich 5 2009 \(L_2\) discrepancy of two-dimensional digitally shifted Hammersley point sets in base \(b\). Zbl 1228.11122Faure, Henri; Pillichshammer, Friedrich 5 2009 Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088Pillichshammer, Friedrich; Steinerberger, Stefan 4 2009 Distribution properties of sequences generated by \(Q\)-additive functions with respect to Cantor representation of integers. Zbl 1228.11114Hofer, Roswitha; Pillichshammer, Friedrich; Pirsic, Gottlieb 3 2009 The average distance between two points. Zbl 1183.52006Burgstaller, Bernhard; Pillichshammer, Friedrich 3 2009 The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091Pillichshammer, Friedrich; Pirsic, Gottlieb 2 2009 Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061Hofinger, Andreas; Pillichshammer, Friedrich 2 2009 Discrepancy of hyperplane nets and cyclic nets. Zbl 1184.65008Pillichshammer, Friedrich; Pirsic, Gottlieb 1 2009 The construction of good extensible rank-1 lattices. Zbl 1211.11092Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J. 21 2008 Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich 7 2008 Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich 7 2008 Tractability properties of the weighted star discrepancy. Zbl 1146.65002Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 6 2008 The weighted dyadic diaphony of digital sequences. Zbl 1228.11118Kritzer, Peter; Pillichshammer, Friedrich 2 2008 The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009Larcher, Gerhard; Pillichshammer, Friedrich 2 2008 Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules. Zbl 1130.65005Dick, Josef; Pillichshammer, Friedrich 18 2007 A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Zbl 1150.11026Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich 7 2007 On the existence of higher order polynomial lattices based on a generalized figure of merit. Zbl 1130.65047Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 6 2007 The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002Cristea, Ligia L.; Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 6 2007 Constructions of general polynomial lattices for multivariate integration. Zbl 1125.65006Kritzer, Peter; Pillichshammer, Friedrich 4 2007 Uniform distribution of sequences connected with the weighted sum-of-digits function. Zbl 1201.11081Pillichshammer, Friedrich 4 2007 Points sets with low \(L_p\) discrepancy. Zbl 1153.11037Kritzer, Peter; Pillichshammer, Friedrich 3 2007 The construction of good extensible Korobov rules. Zbl 1131.11051Dick, J.; Pillichshammer, F.; Waterhouse, B. J. 3 2007 A note on optimal point distributions in \([0,1)^{s}\). Zbl 1201.11084Larcher, Gerhard; Pillichshammer, Friedrich 3 2007 Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 2 2007 A lower bound for the \(b\)-adic diaphony. Zbl 1140.11037Cristea, Ligia L.; Pillichshammer, Friedrich 2 2007 Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 1 2007 Dyadic diaphony of digital sequences. Zbl 1152.11036Pillichshammer, Friedrich 1 2007 Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich 9 2006 An exact formula for \(L_2\) discrepancy of the shifted Hammersley point set. Zbl 1147.11041Kritzer, Peter; Pillichshammer, Friedrich 8 2006 Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich 4 2006 ...and 29 more Documents all cited Publications top 5 cited Publications 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 all top 5 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. 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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. 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Central European Journal of Operations Research 1 Methodology and Computing in Applied Probability 1 Scandinavian Actuarial Journal ...and 21 more Serials all top 5 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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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