Computing Eigenspaces With Low Rank Constraints

DOI10.1137/19M1308384zbMath1462.65039OpenAlexW2995224176MaRDI QIDQ5857626

André Uschmajew, Max Pfeffer, Christian Krumnow

Publication date: 1 April 2021

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

Full work available at URL: https://doi.org/10.1137/19m1308384

zbMATH Keywords

eigenvalue problemlow rank approximationRiemannian optimizationdensity matrix renormalization group algorithm

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical optimization and variational techniques (65K10) Eigenvalues, singular values, and eigenvectors (15A18) Multilinear algebra, tensor calculus (15A69) Methods of local Riemannian geometry (53B21)

Related Items (1)

Low-rank tensor methods for partial differential equations

Uses Software

• Manopt
• lobpcg.m

Cites Work

• Tensor Decompositions and Applications
• Tensor-Train Decomposition
• Tensor numerical methods in scientific computing
• Computation of extreme eigenvalues in higher dimensions using block tensor train format
• The density-matrix renormalization group in the age of matrix product states
• \(O(d \log N)\)-quantics approximation of \(N\)-\(d\) tensors in high-dimensional numerical modeling
• A new scheme for the tensor representation
• On manifolds of tensors of fixed TT-rank
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Low-Rank Matrix Completion by Riemannian Optimization
• Projection-like Retractions on Matrix Manifolds
• The Alternating Linear Scheme for Tensor Optimization in the Tensor Train Format
• Manopt, a Matlab toolbox for optimization on manifolds
• Alternating Minimal Energy Methods for Linear Systems in Higher Dimensions
• Low-Rank Tensor Methods with Subspace Correction for Symmetric Eigenvalue Problems
• Tensor Spaces and Numerical Tensor Calculus
• Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
• The Geometry of Algorithms with Orthogonality Constraints
• Jacobi--Davidson Method on Low-Rank Matrix Manifolds
• An area law for one-dimensional quantum systems
• Corrected One-Site Density Matrix Renormalization Group and Alternating Minimal Energy Algorithm
• Optimization algorithms exploiting unitary constraints
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