Friedrich Pillichshammer

发表

Very low truncation dimension for high dimensional integration under modest error demand

Grzegorz W. Wasilkowski, Peter Kritzer, Friedrich Pillichshammer, 2016, J. Complex..

Truncation dimension for linear problems on multivariate function spaces

Grzegorz W. Wasilkowski, Peter Kritzer, Aicke Hinrichs, 2018, 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 polynomial lattice rules for multivariate integration

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

Tractability properties of the discrepancy in Orlicz norms pdf

Aicke Hinrichs, Josef Dick, Friedrich Pillichshammer, 2020, J. Complex..

The Inverse of the Star-Discrepancy Problem and the Generation of Pseudo-Random Numbers

Josef Dick, Friedrich Pillichshammer, 2014, SETA.

Construction algorithms for higher order polynomial lattice rules

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

On the relation of the spectral test to isotropic discrepancy and Lq-approximation in Sobolev spaces pdf

Friedrich Pillichshammer, Mathias Sonnleitner, 2020, ArXiv.

Component-by-component construction of low-discrepancy point sets of small size

Peter Kritzer, Michael Gnewuch, Benjamin Doerr, 2008, Monte Carlo Methods Appl..

A note on isotropic discrepancy and spectral test of lattice point sets

Friedrich Pillichshammer, Mathias Sonnleitner, 2020, J. Complex..

A Method for Approximate Inversion of the Hyperbolic CDF

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

Explicit constructions of point sets and sequences with low discrepancy

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

On Quasi-Monte Carlo Methods in Weighted ANOVA Spaces pdf

Peter Kritzer, Friedrich Pillichshammer, Greg W. Wasilkowski, 2020, ArXiv.

The Sum of Distances Between Vertices of a Convex Polygon with Unit Perimeter

Friedrich Pillichshammer, Gerhard Larcher, 2008, Am. Math. Mon..

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

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

Truncation in average and worst case settings for special classes of ∞-variate functions

Grzegorz W. Wasilkowski, Peter Kritzer, Friedrich Pillichshammer, 2019, Math. Comput. Simul..

Construction Algorithms for Digital Nets with Low Weighted Star Discrepancy

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

Weighted integration over a cube based on digital nets and sequences pdf

Josef Dick, Friedrich Pillichshammer, 2020, ArXiv.

Integration in Hermite spaces of analytic functions

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

Exponential convergence and tractability of multivariate integration for Korobov spaces

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

Bounds for the weighted Lp discrepancy and tractability of integration

Friedrich Pillichshammer, Gunther Leobacher, 2003, J. Complex..

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

Josef Dick, Friedrich Pillichshammer, Gunther Leobacher, 2018, SIAM J. Numer. Anal..

On the existence and distribution quality of hyperplane sequences

Friedrich Pillichshammer, Gottlieb Pirsic, 2013, Finite Fields Their Appl..

The construction of good extensible Korobov rules

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

Extensible hyperplane nets

Friedrich Pillichshammer, Gottlieb Pirsic, 2011, Finite Fields Their Appl..

Special constructions of digital nets and sequences

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

Monte Carlo and Quasi-Monte Carlo Simulation

Friedrich Pillichshammer, Gunther Leobacher, 2014 .

The construction of good extensible rank-1 lattices

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

Approximation in Hermite spaces of smooth functions

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

Ian Sloan and Lattice Rules

Peter Kritzer, Harald Niederreiter, Friedrich Pillichshammer, 2018 .

A note on equivalence of anchored and ANOVA spaces; lower bounds

Grzegorz W. Wasilkowski, Peter Kritzer, Friedrich Pillichshammer, 2017, J. Complex..

Tractability properties of the weighted star discrepancy of the Halton sequence

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

Smolyak algorithms based on digital (t, α, d)-sequences for multivariate integration

Josef Dick, Friedrich Pillichshammer, Gunther Leobacher, 2007 .

Discrepancy of higher rank polynomial lattice point sets

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

Digital net properties of a polynomial analogue of Frolov's construction

Josef Dick, Friedrich Pillichshammer, Kosuke Suzuki, 2018, Finite Fields Their Appl..

Integration and approximation in cosine spaces of smooth functions

Peter Kritzer, Friedrich Pillichshammer, Christian Irrgeher, 2018, Math. Comput. Simul..

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

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

A lower bound for rank 2 lattice rules

Friedrich Pillichshammer, 2004, Math. Comput..

Proof techniques in quasi-Monte Carlo theory

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

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

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

Lattice rules for nonperiodic smooth integrands

Dirk Nuyens, Josef Dick, Friedrich Pillichshammer, 2014, Numerische Mathematik.

Some highlights of Harald Niederreiter's work

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

Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces

Peter Kritzer, Friedrich Pillichshammer, Peter Hellekalek, 2016, J. Complex..

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

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

Propagation rules for digital nets

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

Numerical integration in log-Korobov and log-cosine spaces

Peter Kritzer, Josef Dick, Friedrich Pillichshammer, 2015, Numerical Algorithms.

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..

Euler's Constant and Averages of Fractional Parts

Friedrich Pillichshammer, 2010, Am. Math. Mon..

Tractability of Multivariate Integration in Hybrid Function Spaces

Peter Kritzer, Friedrich Pillichshammer, 2014, MCQMC.

Connections to other discrete objects

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

A note on Korobov lattice rules for integration of analytic functions pdf

Friedrich Pillichshammer, 2020, ArXiv.

Tractability properties of the weighted star discrepancy

Aicke Hinrichs, Friedrich Pillichshammer, Wolfgang Ch. Schmid, 2008, J. Complex..

Tractability properties of the weighted star discrepancy of regular grids

Friedrich Pillichshammer, 2018, J. Complex..

Cyclic Digital Nets, Hyperplane Nets, and Multivariate Integration in Sobolev Spaces

Josef Dick, Friedrich Pillichshammer, Gottlieb Pirsic, 2006, SIAM J. Numer. Anal..

Applied Algebra and Number Theory

Harald Niederreiter, Chaoping Xing, Arne Winterhof, 2014 .

On efficient weighted integration via a change of variables

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

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.

Tractability of multivariate analytic problems

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

Editorial

Peter Kritzer, Arne Winterhof, Friedrich Pillichshammer, 2018, Math. Comput. Simul..

Tractability of multivariate approximation defined over Hilbert spaces with exponential weights

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

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.

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.

On the root mean square weighted L2 discrepancy of scrambled nets

Friedrich Pillichshammer, 2004, J. Complex..

Learning a function from noisy samples at a finite sparse set of points

Friedrich Pillichshammer, Andreas Hofinger, 2009, J. Approx. Theory.

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..

Approximation of analytic functions in Korobov spaces

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

Diaphony, discrepancy, spectral test and worst-case error

Josef Dick, Friedrich Pillichshammer, 2005, Math. Comput. Simul..

Duality theory and propagation rules for higher order nets

Josef Dick, Friedrich Pillichshammer, Jan Baldeaux, 2011, Discret. Math..

L∞-Approximation in Korobov spaces with exponential weights

Henryk Wozniakowski, Peter Kritzer, Friedrich Pillichshammer, 2017, J. Complex..

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

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

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

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

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

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

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..

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

Friedrich Pillichshammer, Ana-Isabel G'omez, Domingo G'omez-P'erez, 2021, J. Comput. Appl. Math..

Weighted integration over a hyperrectangle based on digital nets and sequences

Josef Dick, Friedrich Pillichshammer, 2021, J. Comput. Appl. Math..

Exact order of extreme $L_p$ discrepancy of infinite sequences in arbitrary dimension

Friedrich Pillichshammer, Ralph Kritzinger, 2021 .

Point sets with optimal order of extreme and periodic discrepancy

Friedrich Pillichshammer, Ralph Kritzinger, 2021 .

Weighted Star Discrepancy of Digital Nets in Prime Bases

Harald Niederreiter, Josef Dick, Friedrich Pillichshammer, 2006 .

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

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

An Extremum Problem for Convex Polygons

Friedrich Pillichshammer, Gerhard Larcher, 2007 .

Precise distribution properties of the van der Corput sequence and related sequences

Michael Drmota, Friedrich Pillichshammer, Gerhard Larcher, 2005 .

Distribution Properties of Generalized van der Corput-Halton Sequences and their Subsequences

Peter Kritzer, Friedrich Pillichshammer, Gerhard Larcher, 2009 .

THE AVERAGE DISTANCE BETWEEN TWO POINTS

Friedrich Pillichshammer, Bernhard Burgstaller, 2009, Bulletin of the Australian Mathematical Society.

The $p$-adic diaphony of the Halton sequence

Friedrich Pillichshammer, 2013 .

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

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

On the sum of squared distances in the Euclidean plane

Friedrich Pillichshammer, 2000 .

Improved upper bounds for the star discrepancy of digital nets in dimension 3

Friedrich Pillichshammer, 2003 .

Discrepancy of Hyperplane Nets and Cyclic Nets

Friedrich Pillichshammer, Gottlieb Pirsic, 2009 .

A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets

Peter Kritzer, Friedrich Pillichshammer, Gerhard Larcher, 2007 .

A note on optimal point distributions in [0,1)s

Friedrich Pillichshammer, Gerhard Larcher, 2007 .

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

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

Constructions of general polynomial lattices for multivariate integration

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

On the discrepancy of (0,1)-sequences

Friedrich Pillichshammer, 2004 .

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

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

On extremal point distributions in the Euclidean plane

Friedrich Pillichshammer, F. Pillichshammer, 2003 .

L_2 discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations

Friedrich Pillichshammer, Wolfgang Ch. Schmid, Gottlieb Pirsic, 2010 .

Construction Algorithms for Good Extensible Lattice Rules

Harald Niederreiter, Friedrich Pillichshammer, 2009 .

Metrical lower bounds on the discrepancy of digital Kronecker-sequences

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

Lp discrepancy of generalized two-dimensional Hammersley point sets

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

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

Peter Kritzer, Friedrich Pillichshammer, Gunther Leobacher, 2013 .

An exact formula for the L_2 discrepancy of the shifted Hammersley point set

Peter Kritzer, Friedrich Pillichshammer, 2006 .

Low discrepancy polynomial lattice point sets

Peter Kritzer, Friedrich Pillichshammer, 2012 .

Bounds for the Quality Parameter of Digital Shift Nets over Z2

Friedrich Pillichshammer, 2002 .

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

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

Polynomial Lattice Point Sets

Friedrich Pillichshammer, F. Pillichshammer, 2012 .