4 papers · 1 filter
Existence of dynamical low-rank approximations to parabolic problems
Markus Bachmayr, Henrik Eisenmann, Emil Kieri +1
The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering al…
Adaptive Low-Rank Approximations for Operator Equations: Accuracy Control and Computational Complexity
Markus Bachmayr, Wolfgang Dahmen
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do no…
Unified Analysis of Periodization-Based Sampling Methods for Matérn Covariances
Markus Bachmayr, Ivan G. Graham, Van Kien Nguyen +1
The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational meth…
Stability of Low-Rank Tensor Representations and Structured Multilevel Preconditioning for Elliptic PDEs
Markus Bachmayr, Vladimir Kazeev
Folding grid value vectors of size into th order tensors of mode sizes , combined with low-rank representation in the tensor train format, has been…