Multivariate Algorithms and Quasi-Monte Carlo Methods

Publications


Peer Reviewed Journal Publication
  • 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.
  • 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.
  • 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.
  • Kritzer, P.; Pillichshammer, F.; Wozniakowski, H. (2017) L_infty-approximation in Korobov spaces with exponential weights. Journal of Complexity, Bd. 41, S. 102-125.
  • 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.
  • Laimer, H. (2017, online: 2016) On combined component-by-component constructions of lattice point sets. Journal of Complexity, Bd. 38, S. 22-30.
  • Kritzer, P.; Niederreiter, H. (2016, online: 2016) Mixed orthogonal arrays, (u,m,e,s)-nets, and (u,e,s)-sequences. Discrete Mathematics, Bd. 339, S. 2199-2208.
  • Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (2016, online: 2016) Very low truncation dimension for high dimensional integration under modest error demand. Journal of Complexity, Bd. 35, S. 63-85.
  • Irrgeher, C.; Kritzer, P.; Pillichshammer, F.; Wozniakowski, H. (2016, online: 2016) Tractability of Multivariate Approximation Defined over Hilbert Spaces with Exponential Weights. Journal of Approximation Theory, Bd. 207, S. 301-338.
  • Irrgeher, C.; Kritzer, P.; Pillichshammer, F.; Wozniakowski, H. (2016, online: 2016) Approximation in Hermite spaces of smooth functions. Journal of Approximation Theory, Bd. 207, S. 98-126.
  • 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.
  • Dick, J.; Kritzer, P. (2016, online: 2015) On a projection-corrected component-by-component construction. Journal of Complexity, Bd. 32, S. 74-80.
  • 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.
  • Dick, J.; Kritzer, P.; Leobacher, G.; Pillichshammer, F. (2015, online: 2015) Numerical integration in log-Korobov and log-cosine spaces. Numerical Algorithms, Bd. 70, S. 753-775.
  • Hinrichs, A.; Kritzer, P.; Pillichshammer, F.; Wasilkowski, G.W. (online: 2018) Truncation Dimension for Linear Problems on Multivariate Function Spaces. Numerical Algorithms, Bd. to appear, S. n.a.
  • Hefter, M.; Herzwurm, A.; Müller-Gronbach, Th. Lower error bounds for strong approximation of scalar SDEs with non-Lipschitziancoefficients. Annals of Applied Probability, Bd. to appear, S. n.a.

Conference Contribution: Publication in Proceedings
  • 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.
  • 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.

Contribution in Collection
  • 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.
  • 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.

Dissertation
  • Laimer, Helene (2017) High-dimensional algorithms-Tractability and componentwise constructions. Doktorarbeit, RICAM, JKU Linz, Linz.

Editorship
  • G. Leobacher, E. Buckwar, P. Kritzer, F. Pillichshammer, A. Winterhof (Hrsg.) (2018, online: 2017) Mathematics and computers in simulation: Special issue 10th IMACS seminar on Monte Carlo methods., 143. Aufl.