Priv.-Doz. Mag. Dr. Peter Kritzer

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Peter Kritzer

Peer Reviewed Journal Publication
  • C. Irrgeher, P. Kritzer, F. Pillichshammer. Integration and approximation in cosine spaces of smooth functions. To appear in Mathematics and Computers in Simulation 143, 35-45, 2018.
  • P. Kritzer, H. Laimer, F. Pillichshammer. Tractability of $L_2$-approximation in hybrid function spaces. To appear in Functiones et Approximatio Commentarii Mathematici, 2017.
  • P. Kritzer, F. Pillichshammer, G.W. Wasilkowski. A note on equivalence of anchored and ANOVA spaces; lower bounds. Journal of Complexity 38, 31--38, 2017.
  • P. Kritzer, F. Pillichshammer, H. Wozniakowski. $L_\infty$-approximation in Korobov spaces with exponential weights. Journal of Complexity 41, 102-125, 2017.
  • J. Dick, P. Kritzer. On a projection-corrected component-by-component construction. Journal of Complexity 32, 74-80, 2016.
  • P. Hellekalek, P. Kritzer, F. Pillichshammer. Open type quasi-Monte Carlo integration based on Halton sequences in weighted Sobolev spaces. Journal of Complexity 33, 169-189, 2016.
  • C. Irrgeher, P. Kritzer, F. Pillichshammer, H. Wozniakowski. Approximation in Hermite spaces of smooth functions. Journal of Approximation Theory 207, 98-126, 2016.
  • C. Irrgeher, P. Kritzer, F. Pillichshammer, H. Wozniakowski. Tractability of multivariate approximation defined over Hilbert spaces with exponential weights. Journal of Approximation Theory 207, 301-338, 2016.
  • P. Kritzer, H. Niederreiter. Mixed orthogonal arrays, (u,m,e,s)-nets, and (u,e,s)-sequences. Discrete Mathematics 339, 2199-2208, 2016.
  • P. Kritzer, F. Pillichshammer, G.W. Wasilkowski. Very low truncation dimension for high dimensional integration under modest error demand. Journal of Complexity 35, 63-85, 2016.
  • J. Dick, P. Kritzer, G. Leobacher, F. Pillichshammer. A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights. Journal of Computational and Applied Mathematics 276, 1-15, 2015.
  • J. Dick, P. Kritzer, G. Leobacher, F. Pillichshammer. Numerical integration in log-Korobov and log-cosine spaces. Numerical Algorithms 70, 753-775, 2015.
  • H. Faure, P. Kritzer, F. Pillichshammer From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules. Indagationes Mathematicae 26, 760-822, 2015.
  • C. Irrgeher, P. Kritzer, G. Leobacher, F. Pillichshammer. Integration in Hermite spaces of analytic functions. Journal of Complexity 31, 380-404, 2015.
  • P. Kritzer, H. Niederreiter. Propagation rules for (u,m,e,s)-nets and (u,e,s)-sequences. Journal of Complexity 31, 457-473, 2015.
  • P. Kritzer, F. Pillichshammer. Component-by-component construction of shifted Halton sequences. Uniform Distribution Theory 10 (2), 45-63, 2015.
  • J. Dick, P. Kritzer, F. Pillichshammer, H. Wozniakowski. Approximation of analytic functions in Korobov spaces. Journal of Complexity 30, 2-28, 2014.
  • P. Kritzer, G. Larcher, F. Pillichshammer. Discrepancy estimates for index-transformed uniformly distributed sequences. Functiones et Approximatio Commentarii Mathematici 51, 197-220, 2014.
  • P. Kritzer, F. Pillichshammer, H. Wozniakowski. Multivariate integration of infinitely many times di erentiable functions in weighted Korobov spaces. Mathematics of Computation 83, 1189-1206, 2014.
  • H. Faure, P. Kritzer. New star discrepancy bounds for (t,m,s)-nets and (t,s)-sequences. Monatshefte für Mathematik 172, 55-75, 2013.
  • P. Kritzer, G. Larcher. On the arrangement of point sets in the unit interval. Manuscripta Mathematica 140, 377-391, 2013.
  • P. Kritzer, F. Pillichshammer. On the existence of low-diaphony sequences made of digital sequences and lattice points. Mathematische Nachrichten 286, 224-235, 2013.
  • J. Dick, P. Kritzer. A higher order Blokh-Zyablov propagation rule for higher order nets. Finite Fields and Their Applications 18, 1169-1183, 2012.
  • P. Hellekalek, P. Kritzer. On the diaphony of some finite hybrid point sets. Acta Arithmetica 156, 257-282, 2012.
  • F.J. Hickernell, P. Kritzer, F.Y. Kuo, D. Nuyens. Weighted compound integration rules with higher order convergence for all N. Numerical Algorithms 59, 161-183, 2012.
  • P. Kritzer. On an example of finite mixed quasi-Monte Carlo point sets. Monatshefte für Mathematik 168, 443-459, 2012.
  • P. Kritzer, F. Pillichshammer. Low discrepancy polynomial lattice point sets. Journal of Number Theory 132, 2510-2534, 2012.
  • R. Hofer, P. Kritzer. On hybrid sequences built from Niederreiter-Halton sequences and Kronecker sequences. Bulletin of the Australian Mathematical Society 84, 238-254, 2011.
  • P. Kritzer. A note on the extreme discrepancy of the Hammersley net in base 2. Uniform Distribution Theory 6 (1), 9-19, 2011.
  • P. Kritzer, F. Pillichshammer. A lower bound on a quantity related to the quality of polynomial lattices. Functiones et Approximatio Commentarii Mathematici 45, 125-137, 2011.
  • P. Kritzer, F. Pillichshammer. On the component by component construction of polynomial lattice point sets for numerical integration in weighted Sobolev spaces. Uniform Distribution Theory 6 (1), 79-100, 2011.
  • J. Dick, P. Kritzer. Duality theory and propagation rules for generalized digital nets. Mathematics of Computation 79, 993-1017, 2010.
  • J. Baldeaux, J. Dick, P. Kritzer. On the approximation of smooth functions using generalized digital nets. Journal of Complexity 25, 544-567, 2009.
  • R. Hofer, P. Kritzer, G. Larcher, F. Pillichshammer. Distribution properties of generalized van der Corput-Halton sequences and their subsequences. International Journal of Number Theory 5, 719-746, 2009.
  • X. Zeng, P. Kritzer, F.J. Hickernell. Spline methods using integration lattices and digital nets. Constructive Approximation 30, 529-555, 2009.
  • B. Doerr, M. Gnewuch, P. Kritzer, F. Pillichshammer. Component-by-component construction of low-discrepancy point sets of small size. Monte Carlo Methods and Applications 14, 129-149, 2008.
  • J. Dick, P. Kritzer, F.Y. Kuo, I.H. Sloan. Lattice-Nyström method for Fredholm integral equations of the second kind with convolution type kernels. Journal of Complexity 23, 752-772, 2007.
  • J. Dick, P. Kritzer, G. Leobacher, F. Pillichshammer. Constructions of general polynomial lattice rules based on the weighted star discrepancy. Finite Fields and Their Applications 13, 1045-1070, 2007.
  • J. Dick, P. Kritzer, F. Pillichshammer, W.Ch. Schmid. On the existence of higher order polynomial lattices based on a generalized figure of merit. Journal of Complexity 23, 581-593, 2007.
  • P. Kritzer, G. Larcher, F. Pillichshammer. A thorough analysis of the discrepancy of shifted Hammersley and van der Corput point sets. Annali di Matematica Pura ed Applicata 186, 229-250, 2007.
  • P. Kritzer, F. Pillichshammer. Constructions of general polynomial lattices for multivariate integration. Bulletin of the Australian Mathematical Society 76, 93-110, 2007.
  • P. Kritzer, F. Pillichshammer. On the weighted dyadic diaphony of digital (t,s)-sequences. Proceedings in Applied Mathematics and Mechanics 7, 1026601-1026602, 2007.
  • P. Kritzer, F. Pillichshammer. Point sets with low L_p-discrepancy. Mathematica Slovaca 57, 11-32, 2007.
  • J. Dick, P. Kritzer. A best possible upper bound on the star discrepancy of (t,m,2)-nets. Monte Carlo Methods and Applications 12, 1{17, 2006.
  • P. Kritzer. Improved upper bounds on the star discrepancy of (t,m,s)-nets and (t,s)-sequences. Journal of Complexity 22, 336-347, 2006.
  • P. Kritzer. On some remarkable properties of the two-dimensional Hammersley point set in base 2. Journal de Theorie des Nombres de Bordeaux 18, 203-221, 2006.
  • P. Kritzer, F. Pillichshammer. An exact formula for the L_2 discrepancy of the shifted Hammersley point set. Uniform Distribution Theory 1, 1-13, 2006
  • J. Dick, P. Kritzer. Star discrepancy estimates for digital (t,m,2)-nets and digital (t,2)-sequences over Z_2. Acta Mathemica Hungarica 109, 239-254, 2005.
  • P. Kritzer. A new upper bound on the star discrepancy of (0,1)-sequences. Integers 5, #A11, 9 pp. (electronic), 2005.
  • P. Kritzer, F. Pillichshammer. Improvements of the discrepancy of the van der Corput sequence. Mathematica Pannonica 16, 179-198, 2005.

Conference Contribution: Publication in Proceedings
  • P. Kritzer, H. Niederreiter, F. Pillichshammer. Ian Sloan and lattice rules. To appear in: J. Dick, F.Y. Kuo, H. Wozniakowski (eds.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, Springer, Cham, 2018.
  • P. Kritzer, F. Pillichshammer, G.W. Wasilkowski. Truncation dimension for function approximation. To appear in: J. Dick, F.Y. Kuo, H. Wozniakowski (eds.), Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, Springer, Cham, 2018.
  • P. Kritzer, F. Pillichshammer. Tractability of multivariate integration in hybrid function spaces. In: R. Cools, D. Nuyens (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2014, 437-454, Springer, Berlin, 2016.
  • P. Kritzer, G. Leobacher, F. Pillichshammer. Component-by-component construction of hybrid point sets based on Hammersley and lattice point sets. In: J. Dick, F.Y. Kuo, G.W. Peters, I.H. Sloan (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2012, 501-515, Springer, Heidelberg, 2013.
  • J. Dick, P. Kritzer, F.Y. Kuo. Approximation of functions using digital nets. In: A. Keller, S. Heinrich, H. Niederreiter (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, 275-297, Springer, Berlin, 2008.
  • P. Kritzer, F. Pillichshammer. The weighted dyadic diaphony of digital sequences. In: A. Keller, S. Heinrich, H. Niederreiter (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, 549-560, Springer, Berlin, 2008.
  • P. Kritzer. On the star discrepancy of digital nets and sequences in three dimensions. In: H. Niederreiter, D. Talay (eds.), Monte Carlo and Quasi-Monte Carlo Methods 2004, 273-287, Springer, Berlin, 2006.

Contribution in Collection
  • H. Faure, P. Kritzer. Discrepancy bounds for low-dimensional point sets. In: G. Larcher, F. Pillichshammer, A. Winterhof, C.P. Xing (eds.), Applied Algebra and Number Theory, 58-90, Cambridge University Press, Cambridge, 2014.
  • P. Kritzer, F. Pillichshammer, H. Wozniakowski. Tractability of multivariate analytic problems. In: P. Kritzer, H. Niederreiter, F. Pillichshammer A. Winterhof (eds.), Uniform Distribution and Quasi-Monte Carlo Methods, 147-170, Radon Series in Computational and Applied Mathematics, DeGruyter, Berlin, 2014.