Trace minimization principles for positive semi-definite pencils

DOI10.1016/j.laa.2012.12.003zbMath1262.15010OpenAlexW2057524212MaRDI QIDQ1940103

Xin Liang, Zhaojun Bai, Ren-Cang Li

Publication date: 5 March 2013

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.12.003

zbMATH Keywords

eigenvalueeigenvectorHermitian matrixpositive semi-definitetrace minimizationHermitian matrix pencil

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Eigenvalues, singular values, and eigenvectors (15A18) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57) Matrix pencils (15A22)

Related Items (14)

A Robust Numerical Algorithm for Computing Maxwell's Transmission Eigenvalue Problems ⋮ Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods ⋮ Extensions of Wielandt’s min–max principles for positive semi-definite pencils ⋮ THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM ⋮ An indefinite variant of LOBPCG for definite matrix pencils ⋮ On generalizing trace minimization principles. II ⋮ Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications ⋮ Linear pencils and quadratic programming problems with a quadratic constraint ⋮ Symplectic eigenvalues of positive-semidefinite matrices and the trace minimization theorem ⋮ Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem ⋮ Preconditioned gradient iterations for the eigenproblem of definite matrix pairs ⋮ A Krylov Subspace Method for Large-Scale Second-Order Cone Linear Complementarity Problem ⋮ On generalizing trace minimization principles ⋮ Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization

Cites Work

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• The perturbation bounds for eigenspaces of a definite matrix-pair
• Perturbation bounds for the definite generalized eigenvalue problem
• A minimax characterization for eigenvalues of Hermitian pencils. II
• Variational principles for indefinite eigenvalue problems
• Trace minimization and definiteness of symmetric pencils
• A note on Stewart's theorem for definite matrix pairs
• A variational principle for eigenvalues of pencils of Hermitian matrices
• A minimax characterization for eigenvalues of Hermitian pencils
• Matrix Analysis
• A Trace Minimization Algorithm for the Generalized Eigenvalue Problem
• On perturbations of matrix pencils with real spectra, a revisit

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