Avoiding breakdown in the CGS algorithm

DOI10.1007/BF02142321zbMath0766.65024OpenAlexW2025687348MaRDI QIDQ1186617

Hassane Sadok, Claude Brezinski

Publication date: 28 June 1992

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02142321

zbMATH Keywords

orthogonal polynomialsnumerical examplesLanczos methodrecurrence relationsconjugate gradient squared method

Mathematics Subject Classification ID

Iterative numerical methods for linear systems (65F10)

Related Items (18)

A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems ⋮ Treatment of near-breakdown in the CGS algorithm ⋮ Look-ahead in Bi-CGSTAB and other product methods for linear systems ⋮ The methods of Vorobyev and Lanczos ⋮ Avoiding breakdown in variants of the BI-CGSTAB algorithm ⋮ A look-ahead strategy for the implementation of some old and new extrapolation methods ⋮ An engineering approach to generalized conjugate gradient methods and beyond ⋮ A theoretical overview of Krylov subspace methods ⋮ A linear system solver based on a modified Krylov subspace method for breakdown recovery ⋮ A unified approach to Krylov subspace methods for solving linear systems ⋮ On quasi-minimal residual approach of iterative algorithms for solving nonsymmetric linear systems ⋮ Avoiding breakdown and near-breakdown in Lanczos type algorithms ⋮ Breakdowns in the implementation of the Lánczos method for solving linear systems ⋮ Lanczos-type algorithms for solving systems of linear equations ⋮ On quasi-orthogonal polynomials of orderr ⋮ On vector Hankel determinants ⋮ A review of formal orthogonality in Lanczos-based methods ⋮ A breakdown-free Lanczos type algorithm for solving linear systems

Uses Software

• CGS
• na1

Cites Work

• A new presentation of orthogonal polynomials with applications to their computation
• Nonsymmetric Lanczos and finding orthogonal polynomials associated with indefinite weights
• Avoiding breakdown and near-breakdown in Lanczos type algorithms
• Polynômes orthogonaux formels - applications
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• How Fast are Nonsymmetric Matrix Iterations?

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