Markus Bachmayr

Publication Activity (10 Years)

Years Active: 2013-2024
Publications (10 Years): 26

Top Topics

High Dimensions

Weighted Least Squares

Top Venues

Found. Comput. Math.

SIAM J. Numer. Anal.

Publications

Markus Bachmayr, Riccardo Bardin, Matthias Schlottbom
Low-rank tensor product Richardson iteration for radiative transfer in plane-parallel geometry. CoRR (2024)
Markus Bachmayr, Martin Eigel, Henrik Eisenmann, Igor Voulis
A convergent adaptive finite element stochastic Galerkin method based on multilevel expansions of random fields. CoRR (2024)
Markus Bachmayr, Manfred Faldum
A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations. J. Complex. 82 (2024)
Markus Bachmayr, Wolfgang Dahmen, Mathias Oster
Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy. CoRR (2024)
Markus Bachmayr, Geneviève Dusson, Christoph Ortner, Jack Thomas
Polynomial approximation of symmetric functions. Math. Comput. 93 (346) (2023)
Markus Bachmayr, Henrik Eisenmann, André Uschmajew
Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations. CoRR (2023)
Markus Bachmayr, Manfred Faldum
A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations. CoRR (2023)
Markus Bachmayr
Low-rank tensor methods for partial differential equations. Acta Numer. 32 (2023)
Geneviève Dusson, Markus Bachmayr, Gábor Csányi, Ralf Drautz, Simon Etter, Cas van der Oord, Christoph Ortner
Atomic cluster expansion: Completeness, efficiency and stability. J. Comput. Phys. 454 (2022)
Markus Bachmayr, Igor Voulis
An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality. CoRR (2021)
Markus Bachmayr, Michael Götte, Max Pfeffer
Particle Number Conservation and Block Structures in Matrix Product States. CoRR (2021)
Markus Bachmayr, Geneviève Dusson, Christoph Ortner
Polynomial Approximation of Symmetric Functions. CoRR (2021)
Markus Bachmayr, Anthony Nouy, Reinhold Schneider
Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions. CoRR (2021)
Markus Bachmayr, Henrik Eisenmann, Emil Kieri, André Uschmajew
Existence of dynamical low-rank approximations to parabolic problems. Math. Comput. 90 (330) (2021)
Markus Bachmayr, Vladimir A. Kazeev
Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs. Found. Comput. Math. 20 (5) (2020)
Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen, Robert Scheichl
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances. SIAM J. Numer. Anal. 58 (5) (2020)
Markus Bachmayr, Ana Djurdjevac
Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere. CoRR (2020)
Markus Bachmayr, Emil Kieri, André Uschmajew
Existence of dynamical low-rank approximations to parabolic problems. CoRR (2020)
Benjamin Arras, Markus Bachmayr, Albert Cohen
Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces. SIAM J. Math. Data Sci. 1 (1) (2019)
Markus Bachmayr, Gábor Csányi, Geneviève Dusson, Simon Etter, Cas van der Oord, Christoph Ortner
Approximation of Potential Energy Surfaces with Spherical Harmonics. CoRR (2019)
Markus Bachmayr, Wolfgang Dahmen
Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity. CoRR (2019)
Markus Bachmayr, Reinhold Schneider
Iterative Methods Based on Soft Thresholding of Hierarchical Tensors. Found. Comput. Math. 17 (4) (2017)
Markus Bachmayr, Albert Cohen, Dinh Dung, Christoph Schwab
Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs. SIAM J. Numer. Anal. 55 (5) (2017)
Markus Bachmayr, Albert Cohen
Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. Math. Comput. 86 (304) (2017)
Markus Bachmayr, Wolfgang Dahmen
Adaptive Low-Rank Methods: Problems on Sobolev Spaces. SIAM J. Numer. Anal. 54 (2) (2016)
Markus Bachmayr, Reinhold Schneider, André Uschmajew
Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations. Found. Comput. Math. 16 (6) (2016)
Markus Bachmayr, Wolfgang Dahmen
Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations. Found. Comput. Math. 15 (4) (2015)
Markus Bachmayr, Huajie Chen, Reinhold Schneider
Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry. Numerische Mathematik 128 (1) (2014)
Markus Bachmayr
Integration of Products of Gaussians and Wavelets with Applications to Electronic Structure Calculations. SIAM J. Numer. Anal. 51 (5) (2013)