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Treatment of near-breakdown in the CGS algorithm

https://doi.org/10.1007/bf02141260
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/978-1-4615-3188-3openalex-snapshot
Effective Polynomial Computation
inferredcites →https://doi.org/10.1007/978-3-0348-6558-6openalex-snapshot
Padé-Type Approximation and General Orthogonal Polynomials
inferredcites →https://doi.org/10.1007/978-94-011-0970-3_5openalex-snapshot
Breakdowns In The Computation Of Orthogonal Polynomials
inferredcites →https://doi.org/10.1007/bf01385699openalex-snapshot
An analysis of the composite step biconjugate gradient method
inferredcites →https://doi.org/10.1007/bf01385846openalex-snapshot
A breakdown-free Lanczos type algorithm for solving linear systems
inferredcites →https://doi.org/10.1007/bf01737161openalex-snapshot
Look-ahead in Bi-CGSTAB and other product methods for linear systems
inferredcites →https://doi.org/10.1007/bf02141258openalex-snapshot
A composite step bi-conjugate gradient algorithm for nonsymmetric linear systems
inferredcites →https://doi.org/10.1007/bf02141259openalex-snapshot
A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems
inferredcites →https://doi.org/10.1007/bf02142321openalex-snapshot
Avoiding breakdown in the CGS algorithm
inferredcites →https://doi.org/10.1007/bf02142322openalex-snapshot
A new presentation of orthogonal polynomials with applications to their computation
inferredcites →https://doi.org/10.1007/bf02142326openalex-snapshot
Avoiding breakdown and near-breakdown in Lanczos type algorithms
inferredcites →https://doi.org/10.1007/bf02144109openalex-snapshot
Extrapolation methods: theory and practice
inferredcites →https://doi.org/10.1007/bf02145381openalex-snapshot
Addendum to “Avoiding breakdown and near-breakdown in Lanczos type algorithms”
inferredcites →https://doi.org/10.1007/bfb0066470openalex-snapshot
Polynômes orthogonaux formels : applications
inferredcites →https://doi.org/10.1007/bfb0080116openalex-snapshot
Conjugate gradient methods for indefinite systems
inferredcites →https://doi.org/10.1007/bfb0090905openalex-snapshot
The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors
inferredcites →https://doi.org/10.1007/s002110050015openalex-snapshot
Hybrid procedures for solving linear systems
inferredcites →https://doi.org/10.1016/0024-3795(80)90165-2openalex-snapshot
Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
inferredcites →https://doi.org/10.1016/0024-3795(83)80026-3openalex-snapshot
On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems
inferredcites →https://doi.org/10.1016/0168-9274(93)90087-8openalex-snapshot
Lanczos-type algorithms for solving systems of linear equations
inferredcites →https://doi.org/10.1016/0378-4754(88)90016-xopenalex-snapshot
Scientific computing on vector computers
inferredcites →https://doi.org/10.1016/0378-4754(88)90070-5openalex-snapshot
Review on stochastic approach to round-off error analysis and its applications
inferredcites →https://doi.org/10.1016/s0898-1221(96)00217-9openalex-snapshot
Breakdowns in the implementation of the Lánczos method for solving linear systems
inferredcites →https://doi.org/10.1017/cbo9781107049949openalex-snapshot
Fourier Analysis
inferredcites →https://doi.org/10.1090/s0025-5718-1985-0771034-2openalex-snapshot
A look-ahead Lánczos algorithm for unsymmetric matrices
inferredcites →https://doi.org/10.1137/0613037openalex-snapshot
A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
inferredcites →https://doi.org/10.1137/0613049openalex-snapshot
How Fast are Nonsymmetric Matrix Iterations?
inferredcites →https://doi.org/10.1137/0910004openalex-snapshot
CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
inferredcites →https://doi.org/10.1137/0912003openalex-snapshot
A Theoretical Comparison of the Arnoldi and GMRES Algorithms
inferredcites →https://doi.org/10.1137/0913035openalex-snapshot
Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
inferredcites →https://doi.org/10.1137/0914009openalex-snapshot
An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
inferredcites →https://doi.org/10.1137/0914062openalex-snapshot
Variants of BICGSTAB for Matrices with Complex Spectrum
inferredcites →https://doi.org/10.1137/0915021openalex-snapshot
Residual Smoothing Techniques for Iterative Methods
inferredcites →https://doi.org/10.1137/s0895479890188803openalex-snapshot
A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II
inferredcites →https://doi.org/10.2118/5729-msopenalex-snapshot
Orthomin, an Iterative Method for Solving Sparse Sets of Simultaneous Linear Equations
inferredcites →https://doi.org/10.2307/2153136openalex-snapshot
Extrapolation Methods: Theory and Practice.
inferredcites →https://doi.org/10.6028/jres.045.026openalex-snapshot
An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
inferredcites →https://doi.org/10.6028/jres.049.006openalex-snapshot
Solution of systems of linear equations by minimized iterations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.1007/978-1-4613-0261-2_8openalex-snapshot
Systems of Linear Algebraic Equations
inferred← citeshttps://doi.org/10.1007/978-3-0348-8685-7_2openalex-snapshot
Transpose-Free Look-Ahead Algorithms for Lanczos’ Method
inferred← citeshttps://doi.org/10.1007/978-94-011-0970-3_5openalex-snapshot
Breakdowns In The Computation Of Orthogonal Polynomials
inferred← citeshttps://doi.org/10.1007/978-94-011-5412-3_4openalex-snapshot
Linear System Solvers: Sparse Iterative Methods
inferred← citeshttps://doi.org/10.1007/bf01737161openalex-snapshot
Look-ahead in Bi-CGSTAB and other product methods for linear systems
inferred← citeshttps://doi.org/10.1007/bf02141259openalex-snapshot
A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems
inferred← citeshttps://doi.org/10.1007/bf02142487openalex-snapshot
A look-ahead strategy for the implementation of some old and new extrapolation methods
inferred← citeshttps://doi.org/10.1007/bf02142491openalex-snapshot
Breakdown and near-breakdown control in the CGS algorithm using stochastic arithmetic
inferred← citeshttps://doi.org/10.1007/s002110050015openalex-snapshot
Hybrid procedures for solving linear systems
inferred← citeshttps://doi.org/10.1016/0024-3795(94)00081-6openalex-snapshot
The methods of Vorobyev and Lanczos
inferred← citeshttps://doi.org/10.1016/0168-9274(95)00085-2openalex-snapshot
An overview of approaches for the stable computation of hybrid BiCG methods
inferred← citeshttps://doi.org/10.1016/0168-9274(95)00110-7openalex-snapshot
Extrapolation algorithms and Padé approximations: a historical survey
inferred← citeshttps://doi.org/10.1016/j.parco.2017.05.006openalex-snapshot
Preconditioned Krylov solvers on GPUs
inferred← citeshttps://doi.org/10.1016/s0024-3795(00)00102-6openalex-snapshot
On vector Hankel determinants
inferred← citeshttps://doi.org/10.1016/s0168-2024(99)80012-5openalex-snapshot
References
inferred← citeshttps://doi.org/10.1016/s0377-0427(01)00412-5openalex-snapshot
A review of formal orthogonality in Lanczos-based methods
inferred← citeshttps://doi.org/10.1016/s0898-1221(96)00217-9openalex-snapshot
Breakdowns in the implementation of the Lánczos method for solving linear systems
inferred← citeshttps://doi.org/10.1016/s1570-8659(02)08003-1openalex-snapshot
Computational methods for large eigenvalue problems
inferred← citeshttps://doi.org/10.1017/s0962492900002737openalex-snapshot
Lanczos-type solvers for nonsymmetric linear systems of equations
inferred← citeshttps://doi.org/10.1023/a:1012085428800openalex-snapshot
Transpose-free Lanczos-type algorithms for nonsymmetric linear systems
inferred← citeshttps://doi.org/10.1023/a:1014832627766openalex-snapshot
On the Vector ε-Algorithm for Solving Linear Systems of Equations
inferred← citeshttps://doi.org/10.1023/a:1022238402573openalex-snapshot
Derivation of BiCG from the conditions defining lanczos' method for solving a system of linear equations
inferred← citeshttps://doi.org/10.1109/ipdpsw.2016.45openalex-snapshot
Efficiency of General Krylov Methods on GPUs -- An Experimental Study
inferred← citeshttps://doi.org/10.1137/s0895479896306744openalex-snapshot
Look-Ahead Procedures for Lanczos-Type Product Methods Based on Three-Term Lanczos Recurrences
inferred← citeshttps://doi.org/10.1137/s1064827596304812openalex-snapshot
QMR Smoothing for Lanczos-Type Product Methods Based on Three-Term Rrecurrences
inferred← citeshttps://doi.org/10.22099/ijsts.2013.1634openalex-snapshot
A preemptive restarting approach to beating the inherent instability of Lanczos-type algorithms
inferred← citeshttps://doi.org/10.4064/-29-1-19-33openalex-snapshot
Orthogonal polynomials and the Lanczos method
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