Peer Reviewed Journal Publication

  • Kritzer, P. (2023, online: 2022) A note on the CBC-DBD construction of lattice rules with general positive weights. Journal of Complexity, Bd. 76, S. 101721.
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  • Krieg, D.; Siedlecki, P.; Ullrich, M.; Wozniakowski, H. (2023) Exponential tractability of L2-approximation with function values. Advances in Computational Mathematics, Bd. 49, S. Article Number 18.
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  • Dolbeault, M.; Krieg, D.; Ullrich, M. (2023, online: 2022) A sharp upper bound for sampling numbers in L_2. Applied and Computational Harmonic Analysis, Bd. 63, S. 113-134.
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  • Ebert, A.; Kritzer, P.; Osisiogu, O.; Stepaniuk, T. (2022, online: 2021) Component-by-component digit-by-digit construction of good polynomial lattice rules in weighted Walsh spaces. Constructive Approximation, Bd. 56, S. 75-119.
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  • Ebert, A.; Kritzer, P.; Osisiogu, O.; Stepaniuk, T. (2022, online: 2021) Construction of good polynomial lattice rules in weighted Walsh spaces by an alternative component-by-component construction. Mathematics and Computers in Simulation, Bd. 192, S. 399-419.
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  • A. Ebert, ; Pillichshammer, F. (2021) Tractability of approximation in the weighted Korobov space in the worst-case setting - a complete picture. Journal of Complexity, Bd. 67, S. 101571.
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  • Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (2021) On quasi-Monte Carlo methods in weighted ANOVA spaces. Mathematics of Computation, Bd. 90, S. 1381-1406.
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  • Wiart, Jaspar; Wong, Elaine (2021, online: 2020) Walsh functions, scrambled (0,m,s)-nets, and negative covariance: applying symbolic computation to quasi-Monte Carlo integration. Mathematics and Computers in Simulation, Bd. 182, S. 277-295.
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  • Ebert, A.; Kritzer, P.; Nuyens, D.; Osisiogu, O. (online: 2021) Digit-by-digit and component-by-component constructions of lattice rules for periodic functions with unknown smoothness. Journal of Complexity, Bd. 66, S. 101555.
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  • P. Kritzer, ; F. Pillichshammer, ; Wozniakowski, H. (2020) Exponential tractability of linear weighted tensor product problemsin the worst-case setting for arbitary linear functionals. Journal of Complexity, Bd. 61, S. 101501.
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  • Serdyuk, A.S.; Stepaniuk, T. (2020) Asymptotically best possible Lebesgue-type inequalities for the Fourier sums on sets of generalized Poisson integrals. Filomat, Bd. 34 (14), S. n.a.
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  • P. Kritzer, ; F. Pillichshammer, ; L. Plaskota, ; Wasilkowski, G.W. (2020) On efficient weighted integration via a change of variables. Numerische Mathematik, Bd. 146, S. 545-570.
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  • P. Kritzer, ; F. Pillichshammer, ; L. Plaskota, ; Wasilkowski, G.W. (2020) On alternative quantization for doubly weighted approximation and integration over unbounded domains. Journal of Approximation Theory, Bd. 256, S. 105433.
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  • Stepaniuk, T. (2020) Hyperuniform point sets on flat tori: deterministic and probabilistic aspects. Constructive Approximation, Bd. 52, S. 313-339.
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  • Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (2019, online: 2018) Truncation in average and worst case settings for special classes of $infty$-variate functions. Mathematics and Computers in Simulations, Bd. 161, S. 52-65.
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  • Kritzer, P.; Wozniakowski, H. (2019, online: 2018) Simple characterizations of exponential tractability for linear multivariate problems. Journal of Complexity, Bd. 51, S. 110-128.
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  • P. Kritzer, ; G. Leobacher, ; M. Szölgyenyi, ; Thonhauser, S. (2019) Approximation methods for piecewise deterministic Markov processes and their costs. Scandinavian Actuarial Journal, Bd. 2019, n. 4, S. 308-335.
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  • Kritzer, P.; Kuo, F.Y.; Nuyens, D.; Ullrich, M. (2019, online: 2018) Lattice rules with random n achieve nearly the optimal O(n^{-alpha-1/2}) error independently of the dimension. Journal of Approximation Theory, Bd. 240, S. 96-113.
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  • Ebert, A.; Kritzer, P. (2019, online: 2018) Constructing lattice points for numerical integration by a reduced fast successive coordinate search algorithm. Journal of Computational and Applied Mathematics, Bd. 351, S. 77-100.
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  • Hefter, M.; Herzwurm, A.; Müller-Gronbach, Th. (2019, online: 2018) Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients. Annals of Applied Probability, Bd. 29, S. 178-216.
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  • Hinrichs, A.; Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (2019, online: 2018) Truncation Dimension for Linear Problems on Multivariate Function Spaces. Numerical Algorithms, Bd. 80, S. 661-685.
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  • Dick, Josef; Irrgeher, Christian; Leobacher, Gunther; Pillichshammer, Friedrich (2018) On the optimal order of integration in Hermite spaces with finite smoothness. SIAM Journal on Numerical Analysis, Bd. 56 (2), S. 684-707.
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  • Kritzer, P.; Laimer, H.; Pillichshammer, F. (2018, online: 2017) Tractability of L_2-approximation in hybrid function spaces. Functiones et Approximatio Commentarii Mathematici, Bd. 58 (1), S. 89-104.
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  • Irrgeher, C.; Kritzer, P.; Pillichshammer, F. (2018, online: 2016) Integration and approximation in cosine spaces of smooth functions. Mathematics and Computers in Simulation, Bd. 143, S. 35-45.
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  • Kritzer, P.; Pillichshammer, F.; Wozniakowski, H. (2017) L_infty-approximation in Korobov spaces with exponential weights. Journal of Complexity, Bd. 41, S. 102-125.
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  • Laimer, H. (2017, online: 2016) On combined component-by-component constructions of lattice point sets. Journal of Complexity, Bd. 38, S. 22-30.
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  • Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (2017, online: 2016) A note on equivalence of anchored and ANOVA spaces; lower bounds. Journal of Complexity, Bd. 38, S. 31-38.
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  • Kritzer, P.; Niederreiter, H. (2016) Mixed orthogonal arrays, (u,m,e,s)-nets, and (u,e,s)-sequences. Discrete Mathematics, Bd. 339, S. 2199-2208.
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  • Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (2016) Very low truncation dimension for high dimensional integration under modest error demand. Journal of Complexity, Bd. 35, S. 63-85.
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  • Irrgeher, C.; Kritzer, P.; Pillichshammer, F.; Wozniakowski, H. (2016) Tractability of Multivariate Approximation Defined over Hilbert Spaces with Exponential Weights. Journal of Approximation Theory, Bd. 207, S. 301-338.
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  • Irrgeher, C.; Kritzer, P.; Pillichshammer, F.; Wozniakowski, H. (2016) Approximation in Hermite spaces of smooth functions. Journal of Approximation Theory, Bd. 207, S. 98-126.
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  • Hellekalek, P.; Kritzer, P.; Pillichshammer, F. (2016, online: 2015) Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Journal of Complexity, Bd. 33, S. 169-189.
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  • Dick, J.; Kritzer, P. (2016, online: 2015) On a projection-corrected component-by-component construction. Journal of Complexity, Bd. 32, S. 74-80.
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  • Dick, J.; Kritzer, P.; Leobacher, G.; Pillichshammer, F. (2015) Numerical integration in log-Korobov and log-cosine spaces. Numerical Algorithms, Bd. 70, S. 753-775.
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  • Faure, H.; Kritzer, P.; Pillichshammer, F. (2015) From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Indagationes Mathematicae, Bd. 26, S. 760-822.
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  • Serdyuk, A.S.; Stepaniuk, T. Uniform approximations by Fourier sums on classes of convolutions of periodic functions. Bulletin de la Societe des Sciences et des Lettres de Lodz. Serie, Recherches sur les Deformations, Bd. to appear, S. n.a.
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  • Kritzer, P.; Osisiogu, O. On a reduced component-by-component digit-by-digit construction of lattice point sets. Uniform Distribution Theory, Bd. n.a., S. to appear.
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Book/Monograph

  • J. Dick, P. Kritzer, F. Pillichshammer (2022) Lattice Rules. In Reihe: Springer Series in Computational Mathematics: Springer Verlag.
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  • F. J. Hickernell, P. Kritzer (eds.) (2020) Multivariate Algorithms and Information-Based Complexity., hrsg. v. Radon Series on Computational and Applied Mathematics, 27; Berlin: de Gruyter.
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Conference Contribution: Publication in Proceedings

  • Ebert, A.; Kritzer, P.; Nuyens, D. (2020) Constructing QMC Finite Element Methods for Elliptic PDEs with Random Coefficients by a Reduced CBC Construction. In: L'Ecuyer, P.; Tuffin, B. (Hrsg.), Monte Carlo and Quasi-Monte Carlo Methods 2018; Cham: Springer, S. 183-205.
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  • Hickernell, F. J.; Kritzer, P.; Wozniakowski, H. (2020, online: 2019) Exponential tractability of linear tensor productproblems. In: Wood, D.R.; DeGier, J.; Praeger, C.; Tao, T. (Hrsg.), 2018 MATRIX Annals; Cham: Springer, S. 61-78.
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  • Kritzinger, R.; Laimer, H.; Neumüller, M. (2018) A reduced fast construction of polynomial lattice point sets with low weighted star discrepancy. In: Glynn, P. and Owen, A.B. (Hrsg.), Monte Carlo and Quasi-Monte Carlo Methods 2016 (MCQMC 2016); Cham: Springer, S. 377-394.
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  • Kritzer, P.; Pillichshammer, F. (2016) Tractability of multivariate integration in hybrid function spaces. In: Cools, R.; Nuyens, D. (Hrsg.), Monte Carlo and Quasi-Monte Carlo Methods 2014 (MCQMC 2014); Berlin: Springer, S. 437-454.
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Contribution in Collection

  • Ebert, A.; Kritzer, P.; Pillichshammer, F. (2022) Tractability of approximation in the weighted Korobov space in the worst-case setting. In: Botev, Z.; Keller, A.; Lemieux, C.; Tuffin, B. (Hrsg.), Advances in Modeling and Simulation; Cham: Springer, S. 131-150.
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  • Stepaniuk, T. (2020) Order estimates of best orthogonal trigonometric approximations of classes of infinitely differentiable functions. In: Raigorodskii, A.M.; Rassias, M. Th. (Hrsg.), Trigonometric Sums and Their Applications; Cham: Springer, S. 273-287.
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  • Ding, Y.; Hickernell, F.J.; Kritzer, P.; Mak, S. (2020) Adaptive approximation for multivariate linear problems with inputs lying in a cone. In: Hickernell, F.J.; Kritzer, P. (Hrsg.), Multivariate Algorithms and Information-Based Complexity; Berlin/Boston: DeGruyter, S. 109-145.
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  • Kritzer, P.; Niederreiter, H.; Pillichshammer, F. (2018) Ian Sloan and Lattice Rules. In: Dick, J.; Kuo, F.Y.; Wozniakowski, H. (Hrsg.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan: Springer, S. 741-769.
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  • Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (2018) Truncation Dimension for Function Approximation. In: Dick, J.; Kuo, F.Y.; Wozniakowski, H. (Hrsg.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan: Springer, S. 771-792.
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Dissertation

  • Anupindi, V. (2022) Linear complexity of some sequences derived from hyperelliptic curves of genus 2. Doktorarbeit, RICAM/Inst. of Financial Math. and Appl. Number Theory, ÖAW/JKU, Linz.
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  • Laimer, Helene (2017) High-dimensional algorithms-Tractability and componentwise constructions. Doktorarbeit, RICAM, JKU Linz, Linz.
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Editorship

  • G. Leobacher, E. Buckwar, P. Kritzer, F. Pillichshammer, A. Winterhof (Hrsg.) (2018) Mathematics and computers in simulation: Special issue 10th IMACS seminar on Monte Carlo methods., 143. Aufl.
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