Integration of Products of Gaussians and Wavelets with Applications to Electronic Structure Calculations. - Markus Bachmayr (SIAM J. Numer. Anal., 2013)

Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry. - Markus Bachmayr; Huajie Chen; Reinhold Schneider (Numerische Mathematik, 2014)

Adaptive Near-Optimal Rank Tensor Approximation for High-Dimensional Operator Equations. - Markus Bachmayr; Wolfgang Dahmen (Found. Comput. Math., 2015)

Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations. - Markus Bachmayr; Reinhold Schneider; André Uschmajew (Found. Comput. Math., 2016)

Adaptive Low-Rank Methods: Problems on Sobolev Spaces. - Markus Bachmayr; Wolfgang Dahmen (SIAM J. Numer. Anal., 2016)

Iterative Methods Based on Soft Thresholding of Hierarchical Tensors. - Markus Bachmayr; Reinhold Schneider (Found. Comput. Math., 2017)

Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. - Markus Bachmayr; Albert Cohen 002 (Math. Comput., 2017)

Fully Discrete Approximation of Parametric and Stochastic Elliptic PDEs. - Markus Bachmayr; Albert Cohen 002; Dinh Dung; Christoph Schwab (SIAM J. Numer. Anal., 2017)

Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity. - Markus Bachmayr; Wolfgang Dahmen (CoRR, 2019)

Approximation of Potential Energy Surfaces with Spherical Harmonics. - Markus Bachmayr; Gábor Csányi; Geneviève Dusson; Simon Etter; Cas van der Oord; Christoph Ortner (CoRR, 2019)

Sequential Sampling for Optimal Weighted Least Squares Approximations in Hierarchical Spaces. - Benjamin Arras; Markus Bachmayr; Albert Cohen 002 (SIAM J. Math. Data Sci., 2019)

Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity. - Markus Bachmayr; Wolfgang Dahmen (75 Years of Mathematics of Computation, 2020)

Existence of dynamical low-rank approximations to parabolic problems. - Markus Bachmayr; Emil Kieri; André Uschmajew (CoRR, 2020)

Multilevel Representations of Isotropic Gaussian Random Fields on the Sphere. - Markus Bachmayr; Ana Djurdjevac (CoRR, 2020)

Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs. - Markus Bachmayr; Vladimir A. Kazeev (Found. Comput. Math., 2020)

Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances. - Markus Bachmayr; Ivan G. Graham; Van Kien Nguyen; Robert Scheichl (SIAM J. Numer. Anal., 2020)

Particle Number Conservation and Block Structures in Matrix Product States. - Markus Bachmayr; Michael Götte; Max Pfeffer (CoRR, 2021)

An adaptive stochastic Galerkin method based on multilevel expansions of random fields: Convergence and optimality. - Markus Bachmayr; Igor Voulis (CoRR, 2021)

Polynomial Approximation of Symmetric Functions. - Markus Bachmayr; Geneviève Dusson; Christoph Ortner (CoRR, 2021)

Approximation by tree tensor networks in high dimensions: Sobolev and compositional functions. - Markus Bachmayr; Anthony Nouy; Reinhold Schneider (CoRR, 2021)

Existence of dynamical low-rank approximations to parabolic problems. - Markus Bachmayr; Henrik Eisenmann; Emil Kieri; André Uschmajew (Math. Comput., 2021)

Atomic cluster expansion: Completeness, efficiency and stability. - Geneviève Dusson; Markus Bachmayr; Gábor Csányi; Ralf Drautz; Simon Etter; Cas van der Oord; Christoph Ortner (J. Comput. Phys., 2022)

Low-rank tensor methods for partial differential equations. - Markus Bachmayr (Acta Numer., 2023)

Polynomial approximation of symmetric functions. - Markus Bachmayr; Geneviève Dusson; Christoph Ortner; Jack Thomas (Math. Comput., 2023)

Low-rank tensor product Richardson iteration for radiative transfer in plane-parallel geometry. - Markus Bachmayr; Riccardo Bardin; Matthias Schlottbom (CoRR, 2024)

Variationally Correct Neural Residual Regression for Parametric PDEs: On the Viability of Controlled Accuracy. - Markus Bachmayr; Wolfgang Dahmen; Mathias Oster (CoRR, 2024)

An adaptive space-time method for nonlinear poroviscoelastic flows with discontinuous porosities. - Markus Bachmayr; Simon Boisserée (CoRR, 2024)

A space-time adaptive low-rank method for high-dimensional parabolic partial differential equations. - Markus Bachmayr; Manfred Faldum (J. Complex., 2024)

A Convergent Adaptive Finite Element Stochastic Galerkin Method Based on Multilevel Expansions of Random Fields. - Markus Bachmayr; Martin Eigel; Henrik Eisenmann; Igor Voulis (SIAM J. Numer. Anal., 2025)

Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients. - Markus Bachmayr; Henrik Eisenmann; Igor Voulis (CoRR, 2025)

Sparse and low-rank approximations of parametric elliptic PDEs: the best of both worlds. - Markus Bachmayr; Huqing Yang (CoRR, 2025)

Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations. - Markus Bachmayr; Henrik Eisenmann; André Uschmajew (Numerische Mathematik, 2025)

Iterative thresholding low-rank time integration. - Markus Bachmayr; Matthieu Dolbeault; Polina Sachsenmaier (CoRR, 2025)