On the singular values of matrices with high displacement rank

DOI10.1016/j.laa.2018.02.025zbMath1446.65022arXiv1712.05864OpenAlexW2963291292WikidataQ130168378 ScholiaQ130168378MaRDI QIDQ1748068

Heather Wilber, Alex Townsend

Publication date: 2 May 2018

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.05864

zbMATH Keywords

displacement structuresingular valuesalternating direction implicit methodSylvester matrix equationlow-rank approximationfast Poisson solver

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix equations and identities (15A24) Numerical methods for low-rank matrix approximation; matrix compression (65F55) Numerical methods for matrix equations (65F45)

Related Items (8)

Parallel Algorithms for Computing the Tensor-Train Decomposition ⋮ Numerical conformal mapping with rational functions ⋮ New applications of matrix methods ⋮ Modified iterations for data-sparse solution of linear systems ⋮ A Low-Rank Technique for Computing the Quasi-Stationary Distribution of Subcritical Galton--Watson Processes ⋮ Bounds on the Singular Values of Matrices with Displacement Structure ⋮ On the Compressibility of Tensors ⋮ Why Are Big Data Matrices Approximately Low Rank?

Uses Software

• DLMF
• Chebfun

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solution of Lyapunov equations by alternating direction implicit iteration
• On low-rank approximability of solutions to high-dimensional operator equations and eigenvalue problems
• Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
• On the ADI method for Sylvester equations
• Near-circularity for the rational Zolotarev problem in the complex plane
• Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
• On the decay rate of Hankel singular values and related issues
• A modified low-rank Smith method for large-scale Lyapunov equations
• Existence and computation of low Kronecker-rank approximations for large linear systems of tensor product structure
• Dimension reduction of large-scale systems. Proceedings of a workshop, Oberwolfach, Germany, October 19--25, 2003.
• Exact matrix completion via convex optimization
• A Fast and Well-Conditioned Spectral Method
• An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
• Computational Methods for Linear Matrix Equations
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• On the efficient computation of high-dimensional integrals and the approximation by exponential sums
• Optimum Alternating-Direction-Implicit Iteration Parameters for a Model Problem
• Two applications of a bound on the Hadamard product with a Cauchy matrix
• On the Singular Values of Matrices with Displacement Structure
• Computing with Functions in Spherical and Polar Geometries II. The Disk
• Matrix Equation $XA + BX = C$
• Approximation of Large-Scale Dynamical Systems
• Computing with Functions in Spherical and Polar Geometries I. The Sphere
• A fast algorithm for particle simulations

This page was built for publication: On the singular values of matrices with high displacement rank