Arnoldi-Riccati method for large eigenvalue problems
type: Item
instance of: scholarly article
title: Arnoldi-Riccati method for large eigenvalue problems
zbMATH Open document ID: 0856.65035
DOI: 10.1007/BF01731935
author: Yanyan Li
published in: BIT
publication date: 1996-10-13T00:00:00Z
review text: The authors propose a new method for computing the largest by absolute value eigenvalue of a large sparse matrix. The method consists of two major steps: a) approximate computation of the corresponding invariant subspace, and b) refinement of the approximation by solving a Riccati equation approximately.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 934139
zbMATH Keywords: Arnoldi-Riccati method
zbMATH Keywords: Krylov subspace
zbMATH Keywords: iterative method
zbMATH Keywords: perturbation
zbMATH Keywords: largest eigenvalue
zbMATH Keywords: large sparse matrix
zbMATH Keywords: invariant subspace
zbMATH Keywords: Riccati equation
reviewed by: Plamen Yalamov
describes a project that uses: eigs
describes a project that uses: IRAM
describes a project that uses: Algorithm 432
describes a project that uses: Harwell-Boeing sparse matrix collection
MaRDI profile type: Publication
cites work: The principle of minimized iterations in the solution of the matrix eigenvalue problem
cites work: Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
cites work: Krylov space methods on state-space control models
cites work: Q3219020
cites work: Three methods for refining estimates of invariant subspaces
cites work: Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration
cites work: A Hessenberg-Schur method for the problem AX + XB= C
cites work: Tchebychev acceleration technique for large scale nonsymmetric matrices
cites work: Arnoldi-Tchebychev procedure for large scale nonsymmetric matrices
cites work: Preconditioned Krylov Subspace Methods for Lyapunov Matrix Equations
cites work: Q4040931
cites work: Krylov-subspace methods for the Sylvester equation
cites work: Krylov Subspace Methods for Solving Large Lyapunov Equations
cites work: Computational aspects of F. L. Bauer's simultaneous iteration method
cites work: Chebyshev Acceleration Techniques for Solving Nonsymmetric Eigenvalue Problems
cites work: Q5751863
cites work: A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices
cites work: Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems
cites work: Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
cites work: Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
cites work: Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices
cites work: Q3998482
description: scientific article; zbMATH DE number 934139