Research Group of Prof. Dr. M. Bachmayr
Institute for Numerical Simulation
maximize

Publications of Prof. Dr. Markus Bachmayr:

Journal Papers:

[1] M. Bachmayr and A. Cohen. Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. Mathematics of Computation, 86:701-724, 2017.
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[2] M. Bachmayr, A. Cohen, and G. Migliorati. Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients. ESAIM Math. Model. Numer. Anal., 51(1):321-339, 2017.
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[3] M. Bachmayr, A. Cohen, R. DeVore, and G. Migliorati. Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients. ESAIM Math. Model. Numer. Anal., 51(1):341-363, 2017.
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[4] M. Bachmayr, A. Cohen, and G. Migliorati. Representations of Gaussian random fields and approximation of elliptic PDEs with lognormal coefficients. J. Fourier Anal. Appl., 2017. To appear.
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[5] M. Bachmayr, A. Cohen, and W. Dahmen. Parametric PDEs: Sparse or low-rank approximations? IMA Journal of Numerical Analysis, 2017. To appear.
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[6] M. Bachmayr, A. Cohen, D. Dũng, and C. Schwab. Fully discrete approximation of parametric and stochastic elliptic PDEs. SIAM J. Numer. Anal., 2017. To appear.
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[7] M. Bachmayr and R. Schneider. Iterative methods based on soft thresholding of hierarchical tensors. Found. Comput. Math., 17(4):1037-1083, 2017.
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[8] M. Bachmayr and W. Dahmen. Adaptive low-rank methods: problems on Sobolev spaces. SIAM J. Numer. Anal., 54(2):744-796, 2016.
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[9] M. Bachmayr and W. Dahmen. Adaptive low-rank methods for problems on Sobolev spaces with error control in L2. ESAIM Math. Model. Numer. Anal., 50(4):1107-1136, 2016.
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[10] M. Bachmayr, R. Schneider, and A. Uschmajew. Tensor networks and hierarchical tensors for the solution of high-dimensional partial differential equations. Found. Comput. Math., 16(6):1423-1472, 2016.
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[11] M. Bachmayr and W. Dahmen. Adaptive near-optimal rank tensor approximation for high-dimensional operator equations. Found. Comput. Math., 15(4):839-898, 2015.
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[12] M. Bachmayr, H. Chen, and R. Schneider. Error estimates for Hermite and even-tempered Gaussian approximations in quantum chemistry. Numer. Math., 128(1):137-165, 2014.
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[13] M. Bachmayr, W. Dahmen, R. DeVore, and L. Grasedyck. Approximation of high-dimensional rank one tensors. Constr. Approx., 39(2):385-395, 2014.
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[14] M. Bachmayr. Integration of products of Gaussians and wavelets with applications to electronic structure calculations. SIAM J. Numer. Anal., 51(5):2491-2513, 2013.
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[15] M. Bachmayr. Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation. ESAIM Math. Model. Numer. Anal., 46(6):1337-1362, 2012.
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[16] M. Bachmayr and M. Burger. Iterative total variation schemes for nonlinear inverse problems. Inverse Problems, 25(10):105004, 26, 2009.
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Thesis:

[1] M. Bachmayr. Adaptive Low-Rank Wavelet Methods and Applications to Two-Electron Schrödinger Equations. PhD thesis, RWTH Aachen, 2012.
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[2] M. Bachmayr. Iterative total variation methods for nonlinear inverse problems. Master's thesis, Johannes Kepler Universität Linz, 2007.
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Other Reports:

[1] M. Bachmayr. Space-parameter-adaptive approximation of affine-parametric elliptic PDEs. In Oberwolfach Report 17/2017, Mathematisches Forschungsinstitut Oberwolfach.
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[2] M. Bachmayr. Kolmogorov widths and low-rank approximations of parametric elliptic PDEs. In Oberwolfach Report 2/2015, Mathematisches Forschungsinstitut Oberwolfach.
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[3] M. Bachmayr. Adaptivity and preconditioning for high-dimensional elliptic partial differential equations. In Oberwolfach Report 24/2014, Mathematisches Forschungsinstitut Oberwolfach.
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[4] M. Bachmayr. Adaptive near-optimal rank tensor approximation for high-dimensional operator equations. In Oberwolfach Report 39/2013, Mathematisches Forschungsinstitut Oberwolfach.
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[5] M. Bachmayr. Hyperbolic wavelet discretization of the electronic Schrödinger equation: Explicit correlation and separable approximation of potentials. In Oberwolfach Report 33/2010, Mathematisches Forschunginstitut Oberwolfach.
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