Gradient flow methods for matrix completion with prescribed eigenvalues.
type: Item
instance of: scholarly article
title: Gradient flow methods for matrix completion with prescribed eigenvalues.
zbMATH Open document ID: 1055.15026
DOI: 10.1016/S0024-3795(03)00393-8
author: Moody T. Chu
author: Fasma Diele
author: Ivonne Sgura
published in: Linear Algebra and its Applications
publication date: 2004-03-14T00:00:00Z
review text: Matrix completion with prescribed eigenvalues is a special type of inverse eigenvalue problem which is a challenging problem both theoretically and computationally. In the present paper, the completion problem is recast as one of minimizing the distance between the isospectral matrices with prescribed eigenvalues and the affined matrices with prescribed entries. In the first part, the authors have chronicled some major developments on this subject in the literature. In the second part, they have proposed a dynamical system of which the trajectory allows one to complete the construction of a matrix numerically even under the situation when no existence theory is available at all. In the third part, numerical experiments seem to suggest that the idea of gradient flow approach can serve as a reasonable means to tackle the most general inverse eigenvalue problems with prescribed entries where the prescribed entries are at arbitrary locations with arbitrary cardinalities.
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F18
zbMATH DE Number: 2056679
zbMATH Keywords: matrix completion
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: gradient flow methods
zbMATH Keywords: numerical experiments
zbMATH Keywords: prescribed entries
zbMATH Keywords: isospectral matrices
Wikidata QID: Q62027889
describes a project that uses: Ode15s
describes a project that uses: ode113
describes a project that uses: MATLAB ODE suite
describes a project that uses: Matlab
describes a project that uses: ode23
describes a project that uses: ode45
describes a project that uses: ode23s
MaRDI profile type: Publication
cites work: A survey of matrix inverse eigenvalue problems
cites work: Constructing a Hermitian Matrix from Its Diagonal Entries and Eigenvalues
cites work: Inverse Eigenvalue Problems
cites work: On constructing matrices with prescribed singular values and diagonal elements
cites work: Structured inverse eigenvalue problems
cites work: Note on an inverse characteristic value problem
cites work: Matrices with Prescribed Entries and Eigenvalues. I
cites work: Matrices with Prescribed Entries and Eigenvalues. II
cites work: Matrices with prescribed entries and eigenvalues. III
cites work: Matrices with prescribed off-diagonal elements
cites work: Inverse eigenvalue problems
cites work: Q3783418
cites work: Ein inverses Eigenwertproblem
cites work: Existence of matrices with prescribed eigenvalues and entries
cites work: Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix
cites work: Q4040931
cites work: Inverse matrix eigenvalue problems
cites work: Eigenvalues of Matrices with Prescribed Entries
cites work: Inequalities: theory of majorization and its applications
cites work: Matrices with Prescribed Characteristic Roots and Diagonal Elements
cites work: Q4801531
cites work: The MATLAB ODE Suite
cites work: On the unsolvability of inverse eigenvalues problems almost everywhere
cites work: Some Results on Matrices with Prescribed Diagonal Elements and Singular Values
cites work: Q3726271
cites work: Singular Values, Diagonal Elements, and Convexity
cites work: An introduction to inverse algebraic eigenvalue problems
cites work: A note on constructing a symmetric matrix with specified diagonal entries and eigenvalues
Recommended article: Enhancing Eigenvalue Approximation by Gradient Recovery
Recommended article: A computational framework of gradient flows for general linear matrix equations
Recommended article: Riemannian gradient descent methods for graph-regularized matrix completion
Recommended article: A new gradient projection method for matrix completion
Recommended article: Singular-value decomposition via gradient and self-equivalent flows
Recommended article: Q3765915
Recommended article: Matrix completion with nonconvex regularization: spectral operators and scalable algorithms
Recommended article: Gradient Flow Approach to Geometric Convergence Analysis of Preconditioned Eigensolvers
Recommended article: A gradient system for low rank matrix completion
Recommended article: Spectral projected gradient methods for generalized tensor eigenvalue complementarity problems
description: scientific article; zbMATH DE number 2056679