Deflated Krylov subspace methods for nearly singular linear systems

DOI10.1007/BF00939836zbMath0804.65031OpenAlexW2092082645MaRDI QIDQ1336066

William W. Symes, Juan C. Meza

Publication date: 1 November 1994

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00939836

zbMATH Keywords

iterative methodssparse matricesKrylov subspace methodsconjugate gradient methodsdeflated decompositionsincomplete orthogonalization methodsnearly singular nonsymmetric linear systems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10)

Related Items (5)

A stabilized GMRES method for singular and severely ill-conditioned systems of linear equations ⋮ Analyzing stationary and periodic solutions of systems of parabolic partial differential equations by using singular subspaces as reduced basis ⋮ Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index ⋮ Domain decomposition methods for mixed finite element approximations of wave problems ⋮ A differential semblance algorithm for the inverse problem of reflection seismology

Uses Software

• LINPACK

Cites Work

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• Deflation Techniques and Block-Elimination Algorithms for Solving Bordered Singular Systems
• Newton-Like Pseudo-Arclength Methods for Computing Simple Turning Points
• Computable Error Bounds for Aggregated Markov Chains
• Deflated Decomposition of Solutions of Nearly Singular Systems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of Equations
• Solution of Homogeneous Systems of Linear Equations Arising from Compartmental Models
• Krylov Subspace Methods for Solving Large Unsymmetric Linear Systems
• On the Implicit Deflation of Nearly Singular Systems of Linear Equations
• Low‐rank revealing QR factorizations
• The principle of minimized iterations in the solution of the matrix eigenvalue problem

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