Trace minimization and definiteness of symmetric pencils

DOI10.1016/0024-3795(93)00126-KzbMath0821.15008MaRDI QIDQ1805221

Krešimir Veselić, Jelisaveta Kovac Striko

Publication date: 28 September 1995

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

zbMATH Keywords

inertiaextremal problemmatrix pencilinterlacing of eigenvaluesminimization of the tracepair of symmetric matrices

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Matrix pencils (15A22)

Related Items (19)

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 ⋮ On contractions in spaces with an indefinite metric: G-norms and spectral radii ⋮ THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM ⋮ An indefinite variant of LOBPCG for definite matrix pencils ⋮ Wielandt and Ky-Fan theorem for matrix pairs. ⋮ On generalizing trace minimization principles. II ⋮ Trace minimization principles for positive semi-definite pencils ⋮ 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 ⋮ Unnamed Item ⋮ Detecting a hyperbolic quadratic eigenvalue problem by using a subspace algorithm ⋮ Preconditioned gradient iterations for the eigenproblem of definite matrix pairs ⋮ Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint ⋮ Singular numbers of contractions in spaces with an indefinite metric and Yamamoto's theorem ⋮ On generalizing trace minimization principles ⋮ Connectivity of Quadratic Hypersurfaces and Its Applications in Optimization, Part I: General Theory ⋮ Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization

Cites Work

• Unnamed Item
• Matrices and indefinite scalar products
• Finding a positive definite linear combination of two Hermitian matrices
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Perturbation bounds for the definite generalized eigenvalue problem
• Some remarks on the spectra of Hermitian matrices
• A Trace Minimization Algorithm for the Generalized Eigenvalue Problem

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