Treatment of near-breakdown in the CGS algorithm
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Publication:1334209
DOI10.1007/BF02141260zbMath0810.65028MaRDI QIDQ1334209
Claude Brezinski, Michela Redivo-Zaglia
Publication date: 9 April 1995
Published in: Numerical Algorithms (Search for Journal in Brave)
orthogonal polynomialsnumerical examplesrecurrence relationsLanczos' methodconjugate gradient squared algorithmCGS algorithmmethod of recursive zoom algorithmnear-breakdown situation
Iterative numerical methods for linear systems (65F10) Orthogonalization in numerical linear algebra (65F25)
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Cites Work
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- Breakdowns in the implementation of the Lánczos method for solving linear systems
- Padé-type approximation and general orthogonal polynomials
- On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
- Review on stochastic approach to round-off error analysis and its applications
- Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
- Avoiding breakdown in the CGS algorithm
- A new presentation of orthogonal polynomials with applications to their computation
- Avoiding breakdown and near-breakdown in Lanczos type algorithms
- Extrapolation methods theory and practice
- Addendum to ``Avoiding breakdown and near-breakdown in Lanczos type algorithms
- Hybrid procedures for solving linear systems
- An analysis of the composite step biconjugate gradient method
- A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems
- Treatment of near-breakdown in the CGS algorithm
- Lanczos-type algorithms for solving systems of linear equations
- Polynômes orthogonaux formels - applications
- Look-ahead in Bi-CGSTAB and other product methods for linear systems
- A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
- CGS, A Fast Lanczos-Type Solver for Nonsymmetric 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
- How Fast are Nonsymmetric Matrix Iterations?
- Variants of BICGSTAB for Matrices with Complex Spectrum
- Residual Smoothing Techniques for Iterative Methods
- An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
- A Theoretical Comparison of the Arnoldi and GMRES Algorithms
