F. Pillichshammer

发表

Introduction to Quasi-Monte Carlo Integration and Applications

G. Leobacher, F. Pillichshammer, 2014 .

A note on the sum of distances under a diameter constraint

F. Pillichshammer, 2001 .

Digital Nets and Sequences: Nets and sequences

F. Pillichshammer, J. Dick, 2010 .

Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration

F. Pillichshammer, J. Dick, 2010 .

Optimal $\mathcal{L}_2$ discrepancy bounds for higher order digital sequences over the finite field $\mathbb{F}_2$

F. Pillichshammer, J. Dick, 2012, 1207.5189.

Discrepancy of Digital Sequences: New Results on a Classical QMC Topic

F. Pillichshammer, 2018, Springer Proceedings in Mathematics & Statistics.

Optimal Lp-discrepancy bounds for second order digital sequences

A. Hinrichs, F. Pillichshammer, J. Dick, 2016, 1601.07281.

Optimal order of $L_p$-discrepancy of digit shifted Hammersley point sets in dimension 2

A. Hinrichs, F. Pillichshammer, Ralph Kritzinger, 2014, 1410.4315.

Discrepancy estimates for index-transformed uniformly distributed sequences

G. Larcher, F. Pillichshammer, P. Kritzer, 2014, 1407.8287.

Discrepancy Theory and Quasi-Monte Carlo Integration

F. Pillichshammer, J. Dick, 2014 .

A metrical lower bound on the star discrepancy of digital sequences

G. Larcher, F. Pillichshammer, 2013, 1302.4251.

L2 DISCREPANCY OF LINEARLY DIGIT SCRAMBLED ZAREMBA POINT SETS

H. Faure, F. Pillichshammer, G. Pirsic, 2011 .

A CHARACTERIZATION OF HIGHER ORDER NETS USING WEYL SUMS AND ITS APPLICATIONS

F. Pillichshammer, J. Dick, Jan Baldeaux, 2010 .

Tractability of L 2-approximation in hybrid function spaces

F. Pillichshammer, P. Kritzer, H. Laimer, 2017 .

Tractability of $\mathbb{L}_2$-approximation in hybrid function spaces

F. Pillichshammer, P. Kritzer, H. Laimer, 2017, 1701.02910.

L∞-Approximation in Korobov spaces with exponential weights

H. Wozniakowski, F. Pillichshammer, P. Kritzer, 2016, Journal of Complexity.

On the existence of low‐diaphony sequences made of digital sequences and lattice point sets

F. Pillichshammer, P. Kritzer, 2013 .

Randomized Smolyak algorithms based on digital sequences for multivariate integration

G. Leobacher, F. Pillichshammer, J. Dick, 2007 .

On the existence of higher order polynomial lattices with large flgure of merit

F. Pillichshammer, J. Dick, P. Kritzer, 2006 .

Approximation in Hermite spaces of smooth functions

Henryk Wozniakowski, Peter Kritzer, Friedrich Pillichshammer, 2015, J. Approx. Theory.

Uniform Distribution and Quasi-Monte Carlo Methods - Discrepancy, Integration and Applications

Peter Kritzer, Harald Niederreiter, Arne Winterhof, 2014, Uniform Distribution and Quasi-Monte Carlo Methods.

The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets

Josef Dick, Friedrich Pillichshammer, Gunther Leobacher, 2006, Numerische Mathematik.

Polynomial Lattice Point Sets

Friedrich Pillichshammer, F. Pillichshammer, 2012 .

Walsh Series Analysis of the L2-Discrepancyof Symmetrisized Point Sets

G. Larcher, F. Pillichshammer, G. Larcher, 2001 .

On the mean square weighted ℒ₂ discrepancy of randomized digital (t,m,s)-nets over ℤ₂

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2005 .

Lattice Point Sets

G. Leobacher, F. Pillichshammer, 2014 .

Component-by-Component Construction of Hybrid Point Sets Based on Hammersley and Lattice Point Sets

Peter Kritzer, Friedrich Pillichshammer, Gunther Leobacher, 2013 .

(t, m, s)-Nets and (t, s)-Sequences

G. Leobacher, F. Pillichshammer, 2014 .

Secure pseudorandom bit generators and point sets with low star-discrepancy

F. Pillichshammer, Ana-Isabel G'omez, Domingo G'omez-P'erez, 2020, J. Comput. Appl. Math..

Extreme and periodic $L_2$ discrepancy of plane point sets

A. Hinrichs, F. Pillichshammer, Ralph Kritzinger, 2020, 2005.09933.

Digital nets in dimension two with the optimal order of L_p discrepancy

F. Pillichshammer, Ralph Kritzinger, 2018, Journal de Théorie des Nombres de Bordeaux.

Metrical Star Discrepancy Bounds for Lacunary Subsequences of Digital Kronecker-Sequences and Polynomial Tractability

F. Pillichshammer, M. Neumüller, 2018, Uniform distribution theory.

Metrical star discrepancy bounds for lacunary subsequences of digital Kronecker-sequences and polynomial tractability

F. Pillichshammer, Mario Neumuller, 2016, 1605.00378.

Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness

A. Hinrichs, F. Pillichshammer, J. Dick, 2016, 1604.08713.

Lp-discrepancy of the symmetrized van der Corput sequence

F. Pillichshammer, Ralph Kritzinger, 2015, 1501.02552.

Component-by-component construction of shifted Halton sequences

F. Pillichshammer, P. Kritzer, 2015, 1501.07377.

A lower bound on a quantity related to the quality of polynomial lattices

F. Pillichshammer, P. Kritzer, 2011 .

$L_2$ discrepancy of generalized Zaremba point sets

H. Faure, F. Pillichshammer, 2011 .

ON THE COMPONENT BY COMPONENT CONSTRUCTION OF POLYNOMIAL LATTICE POINT SETS FOR NUMERICAL INTEGRATION IN WEIGHTED SOBOLEV SPACES

F. Pillichshammer, P. Kritzer, 2011 .

The Weighted Dyadic Diaphony of Digital Sequences

F. Pillichshammer, P. Kritzer, 2008 .

Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions

G. Larcher, F. Pillichshammer, R. Hofer, 2008 .

Weighted Discrepancy and High-Dimensional Numerical Integration

G. Larcher, F. Pillichshammer, K. Scheicher, 2003 .

Weighted Star Discrepancy of Digital Nets in Prime Bases

Harald Niederreiter, Josef Dick, Friedrich Pillichshammer, 2006 .

Digital inversive vectors can achieve strong polynomial tractability for the weighted star discrepancy and for multivariate integration

F. Pillichshammer, Domingo Gómez-Pérez, J. Dick, 2015, 1512.06521.

Construction Algorithms for Generalized Polynomial Lattice Rules

F. Pillichshammer, J. Dick, Jan Baldeaux, 2009 .

Strong tractability of multivariate integration of arbitrary order

F. Pillichshammer, J. Dick, 2007 .

On the existence of hyperplane sequences, with quality parameter and discrepancy bounds

F. Pillichshammer, G. Pirsic, 2012, 1211.3522.

Exponential convergence and tractability of multivariate integration for Korobov spaces

Henryk Wozniakowski, Josef Dick, Friedrich Pillichshammer, 2011, Math. Comput..

Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices

Josef Dick, Friedrich Pillichshammer, Kosuke Suzuki, 2016, ArXiv.

Ian Sloan and Lattice Rules

Peter Kritzer, Harald Niederreiter, Friedrich Pillichshammer, 2018 .

A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights

Peter Kritzer, Josef Dick, Friedrich Pillichshammer, 2014, J. Comput. Appl. Math..

Connections to other discrete objects

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2010 .

Propagation rules for digital nets

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2010 .

Special constructions of digital nets and sequences

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2010 .

On the Optimal Order of Integration in Hermite Spaces with Finite Smoothness

G. Leobacher, F. Pillichshammer, J. Dick, 2016, SIAM J. Numer. Anal..

A maximal Gross-Stadje number in the Euclidean plane

F. Pillichshammer, 2000, Bulletin of the Australian Mathematical Society.

Tractability properties of the discrepancy in Orlicz norms

A. Hinrichs, F. Pillichshammer, J. Dick, 2019, J. Complex..

Lp-discrepancy of the symmetrized van der Corput sequence

F. Pillichshammer, Ralph Kritzinger, 2015, Archiv der Mathematik.

Lattice-based integration algorithms: Kronecker sequences and rank-1 lattices

Mario Ullrich, F. Pillichshammer, J. Dick, 2017, Annali di Matematica Pura ed Applicata (1923 -).

Optimal periodic $L_2$-discrepancy and diaphony bounds for higher order digital sequences

F. Pillichshammer, 2022, 2212.05747.

A metrical lower bound on the star discrepancy of digital sequences

G. Larcher, F. Pillichshammer, 2013, Monatshefte für Mathematik.

Tractability of L2-approximation and integration in weighted Hermite spaces of finite smoothness

G. Leobacher, F. Pillichshammer, Adrian Ebert, 2022, J. Complex..

Optimal Lp-discrepancy bounds for second order digital sequences

A. Hinrichs, F. Pillichshammer, J. Dick, 2017, Israel Journal of Mathematics.

Grid-Based Decimation for Wavelet Transforms With Stably Invertible Implementation

F. Pillichshammer, N. Holighaus, Günther Koliander, 2023, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

Lattice rules for nonperiodic smooth integrands

F. Pillichshammer, J. Dick, Dirk Nuyens, 2013, Numerische Mathematik.

On the -Discrepancy of the Hammersley Point Set

F. Pillichshammer, 2002 .

A characterization of generalized nets using Weyl sums and its applications

F. Pillichshammer, J. Dick, Jan Baldeaux, 2009 .

On Weyl products and uniform distribution modulo one

G. Larcher, R. Tichy, F. Pillichshammer, 2016, Monatshefte für Mathematik.

The BMO-discrepancy suffers from the curse of dimensionality

F. Pillichshammer, 2023, J. Complex..

Quasi-Monte Carlo methods for mixture distributions and approximated distributions via piecewise linear interpolation

F. Pillichshammer, J. Dick, T. Cui, 2023, ArXiv.

From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules

Peter Kritzer, Friedrich Pillichshammer, H. Faure, 2015, 1506.03764.

Proof techniques in quasi-Monte Carlo theory

Aicke Hinrichs, Josef Dick, Friedrich Pillichshammer, 2014, J. Complex..

Uniform Distribution Modulo One

G. Leobacher, F. Pillichshammer, 2014 .

Discrepancy of higher rank polynomial lattice point sets

Friedrich Pillichshammer, Julia Greslehner, F. Pillichshammer, 2012, Monte Carlo Methods Appl..

The construction of good extensible rank-1 lattices

Josef Dick, Friedrich Pillichshammer, Benjamin J. Waterhouse, 2008, Math. Comput..

Constructions of general polynomial lattices for multivariate integration

Peter Kritzer, Friedrich Pillichshammer, F. Pillichshammer, 2007, Bulletin of the Australian Mathematical Society.

On the existence of higher order polynomial lattices based on a generalized figure of merit

Peter Kritzer, Josef Dick, Friedrich Pillichshammer, 2007, J. Complex..

The construction of good extensible Korobov rules

Josef Dick, Friedrich Pillichshammer, Benjamin J. Waterhouse, 2007, Computing.

Construction algorithms for polynomial lattice rules for multivariate integration

Frances Y. Kuo, Josef Dick, Ian H. Sloan, 2005, Math. Comput..

On alternative quantization for doubly weighted approximation and integration over unbounded domains

G. W. Wasilkowski, F. Pillichshammer, P. Kritzer, 2019, J. Approx. Theory.

On efficient weighted integration via a change of variables

Peter Kritzer, G. W. Wasilkowski, Leszek Plaskota, 2018, Numerische Mathematik.

Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

Dirk Nuyens, Josef Dick, Friedrich Pillichshammer, 2011, Numerical Algorithms.

Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2007, J. Complex..

Construction Algorithms for Digital Nets with Low Weighted Star Discrepancy

Josef Dick, Friedrich Pillichshammer, Gunther Leobacher, 2005, SIAM J. Numer. Anal..

Basics of Financial Mathematics

G. Leobacher, F. Pillichshammer, 2014 .

Constructions of general polynomial lattice rules based on the weighted star discrepancy

Peter Kritzer, Josef Dick, Friedrich Pillichshammer, 2007, Finite Fields Their Appl..

Some highlights of Harald Niederreiter's work

Chaoping Xing, Arne Winterhof, Friedrich Pillichshammer, 2014, Applied Algebra and Number Theory.

Tractability of approximation in the weighted Korobov space in the worst-case setting - a complete picture

Friedrich Pillichshammer, Adrian Ebert, F. Pillichshammer, 2021, J. Complex..

Exponential tractability of linear weighted tensor product problems in the worst-case setting for arbitrary linear functionals

Peter Kritzer, Friedrich Pillichshammer, Henryk Wo'zniakowski, 2020, J. Complex..

Multivariate integration in weighted Hilbert spaces based on Walsh functions and weighted Sobolev spaces

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2005, J. Complex..

The weighted star discrepancy of Korobov's $p$-sets

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2014, 1404.0114.

On the mean square weighted L2 discrepancy of randomized digital nets in prime base

Josef Dick, Friedrich Pillichshammer, Ligia L. Cristea, 2006, J. Complex..

L2 Discrepancy of Two-Dimensional Digitally Shifted Hammersley Point Sets in Base b

Friedrich Pillichshammer, H. Faure, F. Pillichshammer, 2009 .

A note on the periodic L2-discrepancy of Korobov's p-sets pdf

Aicke Hinrichs, Josef Dick, Friedrich Pillichshammer, 2020, Archiv der Mathematik.

Construction algorithms for higher order polynomial lattice rules

Josef Dick, Friedrich Pillichshammer, Jan Baldeaux, 2011, J. Complex..

A Method for Approximate Inversion of the Hyperbolic CDF

Friedrich Pillichshammer, Gunther Leobacher, G. Leobacher, 2002, Computing.

Distribution properties of sequences generated by Q-additive functions with respect to Cantor representation of integers

F. Pillichshammer, G. Pirsic, Roswitha Hofer, 2009 .

Sums of distances to the nearest integer and the discrepancy of digital nets

Friedrich Pillichshammer, Gerhard Larcher, G. Larcher, 2003 .

Tractability properties of the weighted star discrepancy of the Halton sequence

Aicke Hinrichs, Shu Tezuka, Friedrich Pillichshammer, 2018, J. Comput. Appl. Math..

Explicit constructions of point sets and sequences with low discrepancy

Josef Dick, Friedrich Pillichshammer, F. Pillichshammer, 2013, Uniform Distribution and Quasi-Monte Carlo Methods.

Lp discrepancy of generalized two-dimensional Hammersley point sets

Friedrich Pillichshammer, H. Faure, F. Pillichshammer, 2009 .

Digital Sequences with Best Possible Order of L 2 ‐Discrepancy

F. Pillichshammer, 2006 .

On the L2-Discrepancy of the Sobol-Hammersley Net in Dimension 3

G. Larcher, F. Pillichshammer, G. Larcher, 2002, J. Complex..

ON THE MULTIVARIABLE GENERALIZATION OF ANDERSON-APOSTOL SUMS

F. Pillichshammer, I. Kiuchi, S. S. Eddin, 2018, 1811.06022.

Metrical lower bounds on the discrepancy of digital Kronecker-sequences

Friedrich Pillichshammer, Gerhard Larcher, G. Larcher, 2013, 1302.5267.

Tractability of approximation in the weighted Korobov space in the worst-case setting

F. Pillichshammer, P. Kritzer, Adrian Ebert, 2022, ArXiv.

Tractability of multivariate approximation defined over Hilbert spaces with exponential weights

Henryk Wozniakowski, Peter Kritzer, Friedrich Pillichshammer, 2015, J. Approx. Theory.

Tractability of multivariate analytic problems

Henryk Wozniakowski, Peter Kritzer, Friedrich Pillichshammer, 2014, Uniform Distribution and Quasi-Monte Carlo Methods.

Multivariate integration of infinitely many times differentiable functions in weighted Korobov spaces

Henryk Wozniakowski, Peter Kritzer, Friedrich Pillichshammer, 2013, Math. Comput..

Approximation of analytic functions in Korobov spaces

Henryk Wozniakowski, Peter Kritzer, Josef Dick, 2012, J. Complex..

Integration in Hermite spaces of analytic functions

Peter Kritzer, Friedrich Pillichshammer, Gunther Leobacher, 2014, J. Complex..

On extremal point distributions in the Euclidean plane

Friedrich Pillichshammer, F. Pillichshammer, 2003 .

Dyadic Diaphony of Digital Nets Over ℤ2

F. Pillichshammer, J. Dick, 2005 .