Lehrveranstaltungen Lebenslauf Publikationen

Lehrveranstaltungen

Sommersemester 2024
Mathematik für Anwender II
Mathematische Software
Numerische Mathematik
Oberseminar Angewandte Analysis

Lebenslauf

Publikationen

Recent Preprints

 

• M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter, G. W. Wasilkowski. Embeddings for Infinite-Dimensional Integration and L_2-Approximation with Increasing Smoothness, submitted September 2018. (Math. ArXiv-Version: arxiv.org/abs/1809.07103)
• B. Doerr, C. Doerr, M. Gnewuch. Probabilistic Lower Discrepancy Bounds for Latin Hypercube Samples, in: J. Dick, F. Y. Kuo, H. Wozniakowski (Eds.), Contemporary Computational Mathematics -- A Celebration of the 80th Birthday of Ian Sloan, 339--350, Springer, 2018. (Math. ArXiv-Version: arxiv.org/abs/1707.08481).
• M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter, G. W. Wasilkowski. Equivalence of Weighted Anchored and ANOVA Spaces of Functions with Mixed Smoothness of Order one in L_p, Journal of Complexity 40, 78-99, 2017. (Math. ArXiv-Version: arxiv.org/abs/1610.07075)
• M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter. Embeddings of Weighted Hilbert Spaces and Applications to Multivariate and Infinite-Dimensional Integration, Journal of Approximation Theory 222, 8-39, 2017. (Math. ArXiv-Version: arxiv.org/abs/1608.00906)

Published Articles

 

• B. Doerr, C. Doerr, M. Gnewuch. Probabilistic Lower Discrepancy Bounds for Latin Hypercube Samples, in: J. Dick, F. Y. Kuo, H. Wozniakowski (Eds.), Contemporary Computational Mathematics -- A Celebration of the 80th Birthday of Ian Sloan, 339--350, Springer, 2018. (arxiv.org/abs/1707.08481)
• M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter. Embeddings of Weighted Hilbert Spaces and Applications to Multivariate and Infinite-Dimensional Integration, Journal of Approximation Theory 222, 8-39, 2017.
• M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter, G. W. Wasilkowski. Equivalence of Weighted Anchored and ANOVA Spaces of Functions with Mixed Smoothness of Order one in L_p, Journal of Complexity 40, 78-99, 2017.
• K. Huthmacher, A. Herzwurm, M. Gnewuch, K. Ritter, B. Rethfeld. Monte Carlo Simulation of Electron Dynamics in Liquid Water, Physica A, Vol. 429, 242 - 251, 2015.
• J. Dick, M. Gnewuch. Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition, Journal of Approximation Theory, Vol. 184, 111-145, 2014. DOI: 10.1016/j.jat.2014.04.014
• J. Dick, M. Gnewuch. Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence, Foundations of Computational Mathematics, Vol. 14, 1027-1077, 2014. DOI: 10.1007/s10208-014-9198-8
• J. Baldeaux, M. Gnewuch. Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition, SIAM Journal of Numerical Analysis 52, Issue 3, 1128-1155, 2014.
• M. Gnewuch, S. Mayer, K. Ritter. On weighted Hilbert spaces and integration of functions of infinitely many variables, Journal of Complexity, Vol. 30, Issue 2, 29-47, 2014.
• C. Doerr, M. Gnewuch, M. Wahlström. Calculation of Discrepancy Measures and Applications, in: W.W.L. Chen, A. Srivastav, G. Travaglini (Eds.), A Panorama of Discrepancy Theory, Lecture Notes in Mathematics 2107, pp 621-678, Springer-Verlag, 2014.
• M. Gnewuch. Lower error bounds for randomized multilevel and changing dimension algorithms, in: J. Dick, F. Y. Kuo, G. W. Peters, I. H. Sloan (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2012, 399-415, Springer-Verlag, 2013.
• M. Gnewuch. Infinite-Dimensional Integration on Weighted Hilbert Spaces, Mathematics of Computation 81, 2175-2205, 2012.
• M. Gnewuch, M. Wahlström, C. Winzen. A new randomized algorithm to approximate the star discrepancy based on threshold accepting, SIAM Journal of Numerical Analysis 50, 781-807, 2012.
• M. Gnewuch. Weighted Geometric Discrepancies and Numerical Integration on Reproducing Kernel Hilbert Spaces, Journal of Complexity, Vol. 28, 2-17, 2012.
• M. Gnewuch. Entropy, Randomization, Derandomization, and Discrepancy., in: L. Plaskota, H. Wozniakowski (Eds.),Monte Carlo and Quasi-Monte Carlo Methods 2010, 43-78, Springer-Verlag, 2012.
• M. Gnewuch, H. Wozniakowski. Quasi-Polynomial Tractability, Journal of Complexity, Vol. 27, 312-330, 2011.
• B. Doerr, M. Gnewuch, M. Wahlström. Algorithmic construction of low-discrepancy point sets via dependent randomized rounding, Journal of Complexity, Vol. 26, 490-507, 2010.
• B. Doerr, M. Gnewuch, M. Wahlström. Implementation of a component-by-component algorithm to generate small low-discrepancy samples, in: P. L'Ecuyer, A. B. Owen (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2008, 323-338, Springer, Berlin Heidelberg, 2009.
• M. Gnewuch, H. Wozniakowski. Generalized Tractability for Multivariate Problems, Part II: Linear Tensor Product Problems, Linear Information, and Unrestricted Tractability, Foundations of Computational Mathematics, Vol. 9, 431-460, 2009.
• M. Gnewuch. On Probabilistic Results for the Discrepancy of a Hybrid-Monte Carlo Sequence, Journal of Complexity, Vol. 25, 312-317, 2009.
• G. Ökten, M. Gnewuch. Correction of a proof in A probabilistic result on the discrepancy of a hybrid-Monte Carlo sequence and applications, Monte Carlo Methods and Applications, Vol. 15, 169-172, 2009.
• M. Gnewuch, A. V. Rosca. On G-discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences, Acta Universitatis Apulensis, Vol. 18, 97-110, 2009.
• M. Gnewuch, A. Srivastav, C. Winzen. Finding Optimal Volume Subintervals with k Points and Calculating the Star Discrepancy are NP-Hard Problems, Journal of Complexity, Vol. 25, 115-127, 2009.
• M. Gnewuch. Construction of Minimal Bracketing Covers for Rectangles, Electronic Journal of Combinatorics, Vol. 15(1), Research Paper 95, 20 pages, 2008.
• 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, Vol. 14, 129-149, 2008.
• M. Gnewuch. Bracketing numbers for axis-parallel boxes and applications to geometric discrepancy, Journal of Complexity, Vol. 24, 154-172, 2008.
• M. Gnewuch, H. Wozniakowski. Generalized Tractability for Linear Functionals, in: A. Keller, S. Heinrich, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, 359-381, Springer, Berlin Heidelberg, 2008.
• B. Doerr, M. Gnewuch. Construction of low-discrepancy point sets of small size by bracketing covers and dependent randomized rounding, in: A. Keller, S. Heinrich, H. Niederreiter (Eds.), Monte Carlo and Quasi-Monte Carlo Methods 2006, 299-312, Springer, Berlin Heidelberg, 2008.
• M. Gnewuch, R. Lindloh, R. Schneider, A. Srivastav. Cubature formulas for function spaces with moderate smoothness, Journal of Complexity, Vol. 23, 828-850, 2007.
• B. Doerr, M. Gnewuch, N. Hebbinghaus, F. Neumann. A Rigorous View On Neutrality, Kay Chen Tan et al. (Eds), Proceedings of the 2007 IEEE Congress on Evolutionary Computation, 2591-2597, Singapore, IEEE Press, Vancouver, BC, Canada, 2007.
• M. Gnewuch, H. Wozniakowski. Generalized Tractability for Multivariate Problems, Part I: Linear Tensor Product Problems and Linear Information, Journal of Complexity, Vol. 23, Issue 2, 262-295, 2007.
• B. Doerr, M. Gnewuch, N. Hebbinghaus. Discrepancy of Symmetric Products of Hypergraphs, Electronic Journal of Combinatorics, Vol. 13, Research Paper 40, 10 pages, 2006.
• M. Gnewuch. Differentiable L^p-functional calculus for certain sums of non-commuting operators, Colloquium Mathematicum, Vol. 105, No. 1, 105-125, 2006.
• B. Doerr, M. Gnewuch, A. Srivastav. Bounds and Constructions for the Star-Discrepancy via Delta-covers, Journal of Complexity, Vol. 21, Issue 5, 691-709, 2005, Elsevier.
• M. Gnewuch. Bounds for the average L^p-extreme and the L^\infty-extreme discrepancy, Electronic Journal of Combinatorics, Vol. 12, Research Paper 54, 11 pages, 2005.
• M. Gnewuch. Spectral multipliers for sub-Laplacians on amenable Lie groups with exponential volume growth, Mathematische Zeitschrift, Vol. 246, No.1-2, 69-83, 2004, Springer-Verlag.

Extended Abstracts and Draft Papers in Proceedings

• M. Gnewuch. Infinite-dimensional integration: Optimal randomized multilevel algorithms in the ANOVA setting and related new results, Dagstuhl Reports, Volume 2, Issue 9 (2012), 208-209.
• M. Gnewuch. Weighted L_2 B discrepancy and approximation of integrals over reproducing kernel Hilbert spaces, In: T. Müller-Gronbach, L. Plaskota, J. F. Traub, Dagstuhl Seminar Proceedings, Seminar 09391, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2009. (For a generalized and extended version see the article "Weighted Geometric Discrepancies and Numerical Integration on Reproducing Kernel Hilbert Spaces".)
• M. Gnewuch. Discrepancy bounds for mixed sequences, In: T. Müller-Gronbach, L. Plaskota, J. F. Traub, Dagstuhl Seminar Proceedings, Seminar 09391, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2009.
• M.Gnewuch. Construction of low-discrepancy point sets of small size, Proc. Appl. Math. Mech. 7, Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007, 1022605-1022606 (2007). (DOI 10.1002/pamm.200700453)
• B. Doerr, M. Gnewuch, N. Hebbinghaus. Discrepancy of Products of Hypergraphs, Discrete Mathematics & Theoretical Computer Science, Proceedings of the European Conference on Combinatorics, Graph Theory and Applications 2005.
• M. Gnewuch. Geometric discrepancies and delta-covers, Oberwolfach Reports 1 (2004), 687-690.

Theses

• High-Dimensional Problems: Multivariate Linear Tensor Product Problems, Multivariate Numerical Integration, and Geometric Discrepancy, Habilitation thesis, Kiel, June 2009.
• Zum differenzierbaren Funktionalkalkül auf Lie-Gruppen mit exponentiellem Volumenwachstum, Dissertation thesis, Kiel, March 2002.
• Die Integralgleichungsmethode für elliptische Randwertprobleme, Diploma thesis (enhanced version), Kiel, February 1998.

Older Preprints and Technical Reports

• M. Gnewuch. On Selfadjointness and Spectral Multipliers for Sums of Non-Commuting Operators, Erwin Schrödinger International Institute for Mathematical Physics, Vienna 2003, ESI-Preprint No.1401. (A revised and shorter version appeared in Colloquium Mathematicum 2006, see category "Articles".)
• M. Gnewuch, S. A. Sauter. Boundary integral equations for second order elliptic boundary value problems, Max Planck Institute for Mathematics in the Sciences, Leipzig 1999, Preprint No.55.