Conjugate gradient methods for the Rayleigh quotient minimization of generalized eigenvalue problems

DOI10.1007/BF02243830zbMath0788.65043OpenAlexW79421561MaRDI QIDQ1308505

Haigang Yang

Publication date: 9 January 1994

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02243830

zbMATH Keywords

convergenceeigenvectorsconjugate gradient methodRayleigh quotientgeneralized eigenvalue problemextreme eigenvalues

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items

A minimization method for the solution of large symmetriric eigenproblems, THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM, Algorithms for recursive/semi-recursive bias-compensating least squares system identification within the errors-in-variables framework, Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Extreme eigenvalues, A block preconditioned steepest descent method for symmetric eigenvalue problems, Safe Triplet Screening for Distance Metric Learning, 3-D nested eigenanalysis on finite element grids

Cites Work

• A multilevel variational method for \(Au=\lambda Bu\) on composite grids
• Simultaneous Rayleigh-quotient minimization methods for Ax=lambdaBx
• Two algorithms for treating \(Ax=\lambda Bx\)
• New iterative methods for solution of the eigenproblem
• [https://portal.mardi4nfdi.de/wiki/Publication:3926873 Simultane Iterationsverfahren f�r gro�e allgemeine Eigenwertprobleme]
• On the Computation of Approximate Eigenvalues and Eigenfunctions of Elliptic Operators by Means of a Multi-Grid Method
• The computational efficiency of a new minimization algorithm for eigenvalue analysis
• Optimal gradient minimization scheme for finite element eigenproblems
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