Preconditioned Low-rank Riemannian Optimization for Linear Systems with Tensor Product Structure

DOI10.1137/15M1032909zbMath1382.65089WikidataQ115246966 ScholiaQ115246966MaRDI QIDQ5739957

Daniel Kressner, Michael Steinlechner, Bart Vandereycken

Publication date: 7 July 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

high dimensionalitytensorsRiemannian optimizationlow rankmatrix product statestensor train

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Iterative numerical methods for linear systems (65F10) Multilinear algebra, tensor calculus (15A69) Real-valued functions on manifolds (58C05) Preconditioners for iterative methods (65F08)

Related Items (21)

Randomized numerical linear algebra: Foundations and algorithms ⋮ Alternating Least Squares as Moving Subspace Correction ⋮ QTT-finite-element approximation for multiscale problems. I: Model problems in one dimension ⋮ Iterative methods based on soft thresholding of hierarchical tensors ⋮ Automatic Differentiation for Riemannian Optimization on Low-Rank Matrix and Tensor-Train Manifolds ⋮ Quantized Tensor FEM for Multiscale Problems: Diffusion Problems in Two and Three Dimensions ⋮ Low-rank tensor methods for partial differential equations ⋮ High-order error function designs to compute time-varying linear matrix equations ⋮ Constrained Optimization with Low-Rank Tensors and Applications to Parametric Problems with PDEs ⋮ Desingularization of Bounded-Rank Matrix Sets ⋮ Low-Rank Tensor Approximation for Chebyshev Interpolation in Parametric Option Pricing ⋮ Low-rank Riemannian eigensolver for high-dimensional Hamiltonians ⋮ Geometric Methods on Low-Rank Matrix and Tensor Manifolds ⋮ Jacobi--Davidson Method on Low-Rank Matrix Manifolds ⋮ On the convergence of Krylov methods with low-rank truncations ⋮ Reduced Basis Methods: From Low-Rank Matrices to Low-Rank Tensors ⋮ Projection methods for dynamical low-rank approximation of high-dimensional problems ⋮ Riemannian Multigrid Line Search for Low-Rank Problems ⋮ Adaptive low-rank approximations for operator equations: Accuracy control and computational complexity ⋮ Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold ⋮ ISLET: Fast and Optimal Low-Rank Tensor Regression via Importance Sketching

Uses Software

• htucker
• LOBPCG
• RTRMC

Cites Work

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