Edit Profile Pillichshammer, Friedrich Compute Distance To: Compute Author ID: 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 Co-Authors 22 single-authored 41 Dick, Josef 38 Kritzer, Peter 20 Larcher, Gerhard 15 Leobacher, Gunther 9 Pirsic, Isabel 8 Hinrichs, Aicke 7 Faure, Henri 7 Woźniakowski, Henryk 6 Wasilkowski, Grzegorz W. 5 Winterhof, Arne 4 Baldeaux, Jan 4 Cristea, Ligia-Loreta 4 Hofer, Roswitha 4 Irrgeher, Christian 4 Kritzinger, Ralph 4 Niederreiter, Harald 3 Schmid, Wolfgang Ch. 2 Drmota, Michael 2 Greslehner, Julia 2 Hellekalek, Peter 2 Markhasin, Lev 2 Nuyens, Dirk 2 Plaskota, Leszek 2 Scheicher, Klaus 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 Burgstaller, Bernhard 1 Dick, Joseph 1 Doerr, Benjamin 1 Gnewuch, Michael 1 Gomez-Perez, Domingo 1 Grabner, Peter J. 1 Hofinger, Andreas 1 Krizer, Peter 1 Kuo, Frances Y. 1 Laimer, Helene 1 Larchner, Gerhard 1 Neumüller, Mario 1 Saad Eddin, Sumaia 1 Schell, Thomas 1 Sloan, Ian Hugh 1 Sonnleitner, Mathias 1 Steinerberger, Stefan 1 Tezuka, Shu 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 all top 5 Fields 108 Number theory (11-XX) 72 Numerical analysis (65-XX) 13 Approximations and expansions (41-XX) 6 Convex and discrete geometry (52-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Functional analysis (46-XX) 5 Probability theory and stochastic processes (60-XX) 4 General and overarching topics; collections (00-XX) 4 Geometry (51-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 History and biography (01-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Field theory and polynomials (12-XX) 1 Algebraic geometry (14-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 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 1282.65012Dick, Josef; Pillichshammer, Friedrich 221 2010 Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021Dick, Josef; Pillichshammer, Friedrich 42 2005 Introduction to quasi-Monte Carlo integration and applications. Zbl 1309.65006Leobacher, Gunther; Pillichshammer, Friedrich 31 2014 Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007Dick, J.; Kuo, F. Y.; Pillichshammer, F.; Sloan, I. H. 31 2005 Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 29 2014 Exponential convergence and tractability of multivariate integration for Korobov spaces. Zbl 1221.65077Dick, Josef; Larcher, Gerhard; Pillichshammer, Friedrich; Woźniakowski, Henryk 26 2011 Approximation of analytic functions in Korobov spaces. Zbl 1342.41021Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 22 2014 The construction of good extensible rank-1 lattices. Zbl 1211.11092Dick, Josef; Pillichshammer, Friedrich; Waterhouse, Benjamin J. 22 2008 Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich 21 2014 Integration in Hermite spaces of analytic functions. Zbl 1316.65034Irrgeher, Christian; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 20 2015 Tractability of multivariate analytic problems. Zbl 1333.65019Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 19 2014 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 15 2012 Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022Irrgeher, 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 1294.11127Dick, 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 1080.11058Dick, Josef; Pillichshammer, Friedrich 13 2005 Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086Dick, Josef; Pillichshammer, Friedrich 12 2014 \(L_2\) discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations. Zbl 1198.11072Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb; Schmid, Wolfgang Ch. 12 2010 Walsh series analysis of the \(L_2\)-discrepancy of symmetrized point sets. Zbl 1108.11309Larcher, G.; Pillichshammer, F. 12 2001 Construction algorithms for higher order polynomial lattice rules. Zbl 1218.65003Baldeaux, Jan; Dick, Josef; Greslehner, Julia; Pillichshammer, Friedrich 11 2011 Precise distribution properties of the van der Corput sequence and related sequences. Zbl 1088.11060Drmota, Michael; Larcher, Gerhard; Pillichshammer, Friedrich 11 2005 Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 11 2005 Sums of distances to the nearest integer and the discrepancy of digital nets. Zbl 1054.11039Larcher, G.; Pillichshammer, F. 11 2003 Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 10 2016 Approximation in Hermite spaces of smooth functions. Zbl 1338.65040Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 10 2016 From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich 9 2015 Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061Dick, Josef; Pillichshammer, Friedrich 9 2014 Cyclic digital nets, hyperplane nets, and multivariate integration in Sobolev spaces. Zbl 1110.11023Pirsic, Gottlieb; Dick, Josef; Pillichshammer, Friedrich 9 2006 On the discrepancy of \((0,1)\)-sequences. Zbl 1048.11061Pillichshammer, Friedrich 9 2004 Bounds for the weighted \(L^p\) discrepancy and tractability of integration. Zbl 1366.11090Leobacher, Gunther; Pillichshammer, Friedrich 8 2003 A note on equivalence of anchored and ANOVA spaces; lower bounds. Zbl 1355.65027Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 7 2017 An exact formula for \(L_2\) discrepancy of the shifted Hammersley point set. Zbl 1147.11041Kritzer, Peter; Pillichshammer, Friedrich 7 2006 Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003Dick, Josef; Pillichshammer, Friedrich 7 2005 On the \(L_p\)-discrepancy of the Hammersley point set. Zbl 1010.11043Pillichshammer, Friedrich 7 2002 The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078Dick, Josef; Pillichshammer, Friedrich 6 2015 Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002Dick, 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 1300.65004Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 6 2015 Duality theory and propagation rules for higher order nets. Zbl 1229.11103Baldeaux, Jan; Dick, Josef; Pillichshammer, Friedrich 6 2011 \(L_p\) discrepancy of generalized two-dimensional Hammersley point sets. Zbl 1175.11042Faure, Henri; Pillichshammer, Friedrich 6 2009 Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich 6 2008 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 A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Zbl 1150.11026Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich 6 2007 The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002Cristea, Ligia L.; Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 6 2007 On the sum of squared distances in the Euclidean plane. Zbl 0966.52007Pillichshammer, Friedrich 6 2000 Optimal order of \(L_p\)-discrepancy of digit shifted Hammersley point sets in dimension 2. Zbl 1340.11062Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich 5 2015 \(L_p\)-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070Kritzinger, Ralph; Pillichshammer, Friedrich 5 2015 Polynomial lattice point sets. Zbl 1294.11129Pillichshammer, Friedrich 5 2012 \(L_2\) discrepancy of two-dimensional digitally shifted Hammersley point sets in base \(b\). Zbl 1228.11122Faure, Henri; Pillichshammer, Friedrich 5 2009 Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich 5 2008 Tractability properties of the weighted star discrepancy. Zbl 1146.65002Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 5 2008 A note on the sum of distances under a diameter constraint. Zbl 1002.51015Pillichshammer, Friedrich 5 2001 A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086Larcher, Gerhard; Pillichshammer, Friedrich 4 2014 Low discrepancy polynomial lattice point sets. Zbl 1256.11042Kritzer, Peter; Pillichshammer, Friedrich 4 2012 Construction algorithms for good extensible lattice rules. Zbl 1247.11100Niederreiter, Harald; Pillichshammer, Friedrich 4 2009 Constructions of general polynomial lattices for multivariate integration. Zbl 1125.65006Kritzer, Peter; Pillichshammer, Friedrich 4 2007 Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich 4 2006 Moments of the weighted sum-of-digits function. Zbl 1092.11007Larcher, Gerhard; Pillichshammer, Friedrich 4 2005 On extremal point disributions in the Euclidean plane. Zbl 1026.52008Pillichshammer, F. 4 2003 Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 3 2019 Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 3 2017 \(\mathbb{L}_\infty\)-approximation in Korobov spaces with exponential weights. Zbl 1367.41024Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 3 2017 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 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 Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088Pillichshammer, Friedrich; Steinerberger, Stefan 3 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 Uniform distribution of sequences connected with the weighted sum-of-digits function. Zbl 1201.11081Pillichshammer, Friedrich 3 2007 A note on optimal point distributions in \([0,1)^{s}\). Zbl 1201.11084Larcher, Gerhard; Pillichshammer, Friedrich 3 2007 The construction of good extensible Korobov rules. Zbl 1131.11051Dick, J.; Pillichshammer, F.; Waterhouse, B. J. 3 2007 Dyadic diaphony of digital nets over \(\mathbb Z_2\). Zbl 1130.11042Dick, Josef; Pillichshammer, Friedrich 3 2005 Improved upper bounds for the star discrepancy of digital nets in dimension 3. Zbl 1054.11040Pillichshammer, Friedrich 3 2003 Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu 2 2019 Truncation dimension for function approximation. Zbl 1405.65021Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W. 2 2018 Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 2 2017 Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002Hellekalek, Peter; Kritzer, Peter; Pillichshammer, Friedrich 2 2016 Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050Larcher, Gerhard; Pillichshammer, Friedrich 2 2014 The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048Dick, 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 1291.11003Kritzer, 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 1302.65012Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 2 2013 On the discrepancy of the van der Corput sequence indexed by Fibonacci numbers. Zbl 1290.11111Pillichshammer, Friedrich 2 2012 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 Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061Hofinger, Andreas; Pillichshammer, Friedrich 2 2009 The average distance between two points. Zbl 1183.52006Burgstaller, Bernhard; Pillichshammer, Friedrich 2 2009 The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091Pillichshammer, Friedrich; Pirsic, Gottlieb 2 2009 The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009Larcher, Gerhard; Pillichshammer, Friedrich 2 2008 The weighted dyadic diaphony of digital sequences. Zbl 1228.11118Kritzer, Peter; Pillichshammer, Friedrich 2 2008 Constructions of general polynomial lattice rules based on the weighted star discrepancy. Zbl 1132.11039Dick, Josef; Kritzer, Peter; Leobacher, Gunther; Pillichshammer, Friedrich 2 2007 Points sets with low \(L_p\) discrepancy. Zbl 1153.11037Kritzer, Peter; Pillichshammer, Friedrich 2 2007 Improvements of the discrepancy of the van der Corput sequence. Zbl 1119.11045Kritzer, Peter; Pillichshammer, Friedrich 2 2005 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 Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 07099381Neumüller, Mario; Pillichshammer, Friedrich 1 2018 Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015Pillichshammer, Friedrich 1 2018 On Weyl products and uniform distribution modulo one. Zbl 1410.11106Aistleitner, 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 1428.11136Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne 1 2017 Tractability of multivariate integration in hybrid function spaces. Zbl 1356.65009Kritzer, Peter; Pillichshammer, Friedrich 1 2016 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 Truncation dimension for linear problems on multivariate function spaces. Zbl 1415.65034Hinrichs, Aicke; Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 3 2019 Tractability properties of the weighted star discrepancy of the Halton sequence. Zbl 1443.11152Hinrichs, Aicke; Pillichshammer, Friedrich; Tezuka, Shu 2 2019 Truncation dimension for function approximation. Zbl 1405.65021Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, Grzegorz W. 2 2018 Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability. Zbl 07099381Neumüller, Mario; Pillichshammer, Friedrich 1 2018 Tractability properties of the weighted star discrepancy of regular grids. Zbl 1398.65015Pillichshammer, Friedrich 1 2018 On Weyl products and uniform distribution modulo one. Zbl 1410.11106Aistleitner, 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 1355.65027Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 7 2017 Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences. Zbl 1394.11060Dick, Josef; Hinrichs, Aicke; Markhasin, Lev; Pillichshammer, Friedrich 3 2017 \(\mathbb{L}_\infty\)-approximation in Korobov spaces with exponential weights. Zbl 1367.41024Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 3 2017 Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness. Zbl 1388.11044Dick, 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 1428.11136Dick, Josef; Gomez-Perez, Domingo; Pillichshammer, Friedrich; Winterhof, Arne 1 2017 Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Zbl 1342.41022Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 14 2016 Very low truncation dimension for high dimensional integration under modest error demand. Zbl 1342.65098Kritzer, Peter; Pillichshammer, Friedrich; Wasilkowski, G. W. 10 2016 Approximation in Hermite spaces of smooth functions. Zbl 1338.65040Irrgeher, Christian; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 10 2016 Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Zbl 1353.65002Hellekalek, 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 20 2015 From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Zbl 1335.11063Faure, Henri; Kritzer, Peter; Pillichshammer, Friedrich 9 2015 The weighted star discrepancy of Korobov’s \(p\)-sets. Zbl 1329.11078Dick, Josef; Pillichshammer, Friedrich 6 2015 Proof techniques in quasi-Monte Carlo theory. Zbl 1316.65002Dick, 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 1300.65004Dick, 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 1340.11062Hinrichs, Aicke; Kritzinger, Ralph; Pillichshammer, Friedrich 5 2015 \(L_p\)-discrepancy of the symmetrized van der Corput sequence. Zbl 1320.11070Kritzinger, Ralph; Pillichshammer, Friedrich 5 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 31 2014 Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces. Zbl 1342.65089Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 29 2014 Approximation of analytic functions in Korobov spaces. Zbl 1342.41021Dick, Josef; Kritzer, Peter; Pillichshammer, Friedrich; Woźniakowski, Henryk 22 2014 Lattice rules for nonperiodic smooth integrands. Zbl 1345.65070Dick, Josef; Nuyens, Dirk; Pillichshammer, Friedrich 21 2014 Tractability of multivariate analytic problems. Zbl 1333.65019Kritzer, 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 1294.11127Dick, Josef; Pillichshammer, Friedrich 13 2014 Discrepancy theory and quasi-Monte Carlo integration. Zbl 1358.11086Dick, Josef; Pillichshammer, Friedrich 12 2014 Explicit constructions of point sets and sequences with low discrepancy. Zbl 1335.11061Dick, Josef; Pillichshammer, Friedrich 9 2014 A metrical lower bound on the star discrepancy of digital sequences. Zbl 1293.11086Larcher, Gerhard; Pillichshammer, Friedrich 4 2014 Metrical lower bounds on the discrepancy of digital Kronecker-sequences. Zbl 1385.11050Larcher, Gerhard; Pillichshammer, Friedrich 2 2014 The inverse of the star-discrepancy problem and the generation of pseudo-random numbers. Zbl 1337.11048Dick, 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 1291.11003Kritzer, Peter (ed.); Niederreiter, Harald (ed.); Pillichshammer, Friedrich (ed.); Winterhof, Arne (ed.) 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 15 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 26 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 \(L_2\) discrepancy of generalized Zaremba point sets. Zbl 1277.11081Faure, Henri; Pillichshammer, Friedrich 1 2011 \(L_2\) discrepancy of linearly digit scrambled Zaremba point sets. Zbl 1333.11070Faure, Henri; Pillichshammer, Friedrich; Pirsic, Gottlieb 1 2011 A lower bound on a quantity related to the quality of polynomial lattices. Zbl 1247.11097Kritzer, Peter; Pillichshammer, Friedrich 1 2011 Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. Zbl 1282.65012Dick, Josef; Pillichshammer, Friedrich 221 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. 12 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 6 2009 \(L_2\) discrepancy of two-dimensional digitally shifted Hammersley point sets in base \(b\). Zbl 1228.11122Faure, Henri; Pillichshammer, Friedrich 5 2009 Construction algorithms for good extensible lattice rules. Zbl 1247.11100Niederreiter, Harald; Pillichshammer, Friedrich 4 2009 Average distance between consecutive points of uniformly distributed sequences. Zbl 1208.11088Pillichshammer, Friedrich; Steinerberger, Stefan 3 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 Learning a function from noisy samples at a finite sparse set of points. Zbl 1205.94061Hofinger, Andreas; Pillichshammer, Friedrich 2 2009 The average distance between two points. Zbl 1183.52006Burgstaller, Bernhard; Pillichshammer, Friedrich 2 2009 The quality parameter of cyclic nets and hyperplane nets. Zbl 1208.11091Pillichshammer, Friedrich; Pirsic, Gottlieb 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. 22 2008 Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions. Zbl 1169.11006Hofer, Roswitha; Larcher, Gerhard; Pillichshammer, Friedrich 6 2008 Component-by-component construction of low-discrepancy point sets of small size. Zbl 1156.11030Doerr, Benjamin; Gnewuch, Michael; Kritzer, Peter; Pillichshammer, Friedrich 5 2008 Tractability properties of the weighted star discrepancy. Zbl 1146.65002Hinrichs, Aicke; Pillichshammer, Friedrich; Schmid, Wolfgang Ch. 5 2008 The sum of distances between vertices of a convex polygon with unit perimeter. Zbl 1143.52009Larcher, Gerhard; Pillichshammer, Friedrich 2 2008 The weighted dyadic diaphony of digital sequences. Zbl 1228.11118Kritzer, Peter; 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 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 A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Zbl 1150.11026Kritzer, Peter; Larcher, Gerhard; Pillichshammer, Friedrich 6 2007 The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets. Zbl 1111.65002Cristea, 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 3 2007 A note on optimal point distributions in \([0,1)^{s}\). Zbl 1201.11084Larcher, Gerhard; Pillichshammer, Friedrich 3 2007 The construction of good extensible Korobov rules. Zbl 1131.11051Dick, J.; Pillichshammer, F.; Waterhouse, B. J. 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 Points sets with low \(L_p\) discrepancy. Zbl 1153.11037Kritzer, Peter; Pillichshammer, Friedrich 2 2007 Dyadic diaphony of digital sequences. Zbl 1152.11036Pillichshammer, Friedrich 1 2007 A lower bound for the \(b\)-adic diaphony. Zbl 1140.11037Cristea, Ligia L.; Pillichshammer, Friedrich 1 2007 Randomized Smolyak algorithms based on digital sequences for multivariate integration. Zbl 1134.65006Dick, Josef; Leobacher, Gunther; Pillichshammer, 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 7 2006 Weighted star discrepancy of digital nets in prime bases. Zbl 1096.11025Dick, Josef; Niederreiter, Harald; Pillichshammer, Friedrich 4 2006 An extremum problem for convex polygons. Zbl 1165.51008Larcher, Gerhard; Pillichshammer, Friedrich 1 2006 Digital sequences with best possible order of \(L_2\)-discrepancy. Zbl 1121.11049Pillichshammer, Friedrich 1 2006 Periodic functions with bounded remainder. Zbl 1115.11044Dick, Josef; Pillichshammer, Friedrich 1 2006 On the mean square weighted \(\mathcal {L}_2\) discrepancy of randomized digital nets in prime base. Zbl 1142.11345Cristea, Ligia L.; Dick, Josef; Pillichshammer, Friedrich 1 2006 Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces. Zbl 1085.41021Dick, Josef; Pillichshammer, Friedrich 42 2005 Construction algorithms for polynomial lattice rules for multivariate integration. Zbl 1079.65007Dick, 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 1080.11058Dick, Josef; Pillichshammer, Friedrich 13 2005 Precise distribution properties of the van der Corput sequence and related sequences. Zbl 1088.11060Drmota, Michael; Larcher, Gerhard; Pillichshammer, Friedrich 11 2005 Construction algorithms for digital nets with low weighted star discrepancy. Zbl 1084.11040Dick, Josef; Leobacher, Gunther; Pillichshammer, Friedrich 11 2005 Diaphony, discrepancy, spectral test and worst-case error. Zbl 1193.65003Dick, Josef; Pillichshammer, Friedrich 7 2005 Moments of the weighted sum-of-digits function. Zbl 1092.11007Larcher, Gerhard; Pillichshammer, Friedrich 4 2005 ...and 18 more Documents all cited Publications top 5 cited Publications 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. 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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 all top 5 Cited in 34 Fields 244 Numerical analysis (65-XX) 168 Number theory (11-XX) 76 Approximations and expansions (41-XX) 38 Probability theory and stochastic processes (60-XX) 33 Statistics (62-XX) 29 Functional analysis (46-XX) 25 Harmonic analysis on Euclidean spaces (42-XX) 24 Computer science (68-XX) 14 Operations research, mathematical programming (90-XX) 13 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Partial differential equations (35-XX) 9 Information and communication theory, circuits (94-XX) 7 Combinatorics (05-XX) 5 Convex and discrete geometry (52-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Real functions (26-XX) 4 Operator theory (47-XX) 4 Geometry (51-XX) 4 Quantum theory (81-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 3 Measure and integration (28-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 2 Systems theory; control (93-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Abstract harmonic analysis (43-XX) 1 Integral equations (45-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-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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