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A breakdown-free Lanczos type algorithm for solving linear systems

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

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/bf01385846openalex-snapshot
A breakdown-free Lanczos type algorithm for solving linear systems
inferredcites →https://doi.org/10.1007/bf01385881openalex-snapshot
Orthogonal polynomials: Variable-signed weight functions
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/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
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Conjugate gradient methods for indefinite systems
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Some determinantal identities in a vector space, with applications
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Moment methods in Padé approximation
inferredcites →https://doi.org/10.1016/0024-3795(80)90165-2openalex-snapshot
Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
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Other manifestations of the Schur complement
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/b978-0-12-407475-0.50016-4openalex-snapshot
Iterative Methods for Nonsymmetric Linear Systems
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/10.1137/0719031openalex-snapshot
The Lanczos Biorthogonalization Algorithm and Other Oblique Projection Methods for Solving Large Unsymmetric Systems
inferredcites →https://doi.org/10.1137/0904039openalex-snapshot
The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity
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/s0895479890188803openalex-snapshot
A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms. Part II
inferredcites →https://doi.org/10.2307/2003785openalex-snapshot
Computational Methods of Linear Algebra
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Computational Methods of Linear Algebra.
inferredcites →https://doi.org/10.2307/2004791openalex-snapshot
Method of Moments in Applied Mathematics
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Biorthogonality and Its Applications to Numerical Analysis.
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.

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Recent computational developments in Krylov subspace methods for linear systems
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Stabilized Krylov Subspace Recurrences via Randomized Sketching
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Least Squares Orthogonal Polynomials
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Recent Advances in Lanczos-Based Iterative Methods for Nonsymmetric Linear Systems
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Systems of Linear Algebraic Equations
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Regularization of Ill-Conditioned Systems
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Transpose-Free Look-Ahead Algorithms for Lanczos’ Method
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Breakdowns In The Computation Of Orthogonal Polynomials
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An analysis of the composite step biconjugate gradient method
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Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems
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Look-ahead in Bi-CGSTAB and other product methods for linear systems
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Iterative methods for solvingAx=b, GMRES/FOM versus QMR/BiCG
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A composite step conjugate gradients squared algorithm for solving nonsymmetric linear systems
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Treatment of near-breakdown in the CGS algorithm
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A linear system solver based on a modified Krylov subspace method for breakdown recovery
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Avoiding breakdown in the CGS algorithm
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A new presentation of orthogonal polynomials with applications to their computation
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Avoiding breakdown and near-breakdown in Lanczos type algorithms
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A look-ahead strategy for the implementation of some old and new extrapolation methods
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Formal orthogonal polynomials revisited. Applications
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The Gauss quadrature for general linear functionals, Lanczos algorithm, and minimal partial realization
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A Lanczos-like method for non-autonomous linear ordinary differential equations
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Matrix recursive projection and interpolation algorithms
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Lanczos-type algorithms for solving systems of linear equations
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A theoretical overview of Krylov subspace methods
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Least-squares orthogonal polynomials
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A new taxonomy of conjugate gradient methods
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Iterative solution of linear systems in the 20th century
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