On the squared unsymmetric Lanczos method

DOI10.1016/0377-0427(94)90395-6zbMath0836.65045OpenAlexW1964556214MaRDI QIDQ1347170

Anthony Theodore Chronopoulos

Publication date: 29 April 1996

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(94)90395-6

zbMATH Keywords

linear systemseigenvaluesnumerical testsKrylov subspace methodsbiorthogonal Lanczos methodrestarting processessquared unsymmetric Lanczos method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)

Related Items

Biconjugate residual algorithm for solving general Sylvester-transpose matrix equations ⋮ Conjugate gradient-like methods for solving general tensor equation with Einstein product ⋮ Modified block product preconditioner for a class of complex symmetric linear systems ⋮ Solving constrained quadratic inverse eigenvalue problem via conjugate direction method ⋮ Conjugate gradient-like algorithms for constrained operator equation related to quadratic inverse eigenvalue problems ⋮ Least squares solutions of quadratic inverse eigenvalue problem with partially bisymmetric matrices under prescribed submatrix constraints ⋮ Domain decomposition and parallel processing of a finite element model of the shallow water equations ⋮ Tensor Bi-CR Methods for Solutions of High Order Tensor Equation Accompanied by Einstein Product

Uses Software

• CGS

Cites Work

• Unnamed Item
• A generalized conjugate gradient, least square method
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• An efficient nonsymmetric Lanczos method on parallel vector computers
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems
• s-Step Iterative Methods for (Non)Symmetric (In)Definite Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
• Solution of Sparse Indefinite Systems of Linear Equations
• A Lanczos Method for a Class of Nonsymmetric Systems of Linear Equations
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems

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