Results 91 to 100 of about 281 (133)
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Computing in Science and Engineering, 2000
This survey article reviews the history and current importance of Krylov subspace iteration algorithms.
H A Van Der Vorst
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This survey article reviews the history and current importance of Krylov subspace iteration algorithms.
H A Van Der Vorst
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Krylov subspaces and the analytic grade
Numerical Linear Algebra with Applications, 2005Typical behaviour of the solution of a linear system of equations obtained iteratively by Krylov methods can be characterized by three stages. Initially the residual diminishes steadily; this is followed by stagnation and finally rapid convergence near the algebraic grade.
Milos Ilic, Ian W. Turner
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Deflated and Augmented Krylov Subspace Techniques
Numerical Linear Algebra With Applications, 1997[Shortened review. The full version is available at Zbl ] The paper deals with the general framework of augmenting the Krylov subspace method when solving large and sparse nonsymmetric systems of linear algebraic equations. Three techniques proposed in order to increase the robustness of Krylov subspace methods are explained from the unifying point of ...
Yousef Saad
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Adaptive detectors in the Krylov subspace
Science China Information Sciences, 2014The validity of the application of the Krylov subspace techniques in adaptive filtering and detection is investigated. A new verification of the equivalence of two well-known methods in the Krylov subspace, namely the multistage Wiener filters (MWF) and the auxiliary-vector filtering (AVF), is given in this paper.
Weijian Liu 0001 +4 more
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On Moment Methods in Krylov Subspaces
Doklady Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Krylov Subspace Method for Information Retrieval
SIAM Journal on Matrix Analysis and Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Katarina Blom, Axel Ruhe
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Projection Methods in Krylov Subspaces
Journal of Mathematical Sciences, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Spectral Variants of Krylov Subspace Methods
Numerical Algorithms, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brígida Molina, Marcos Raydan
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2020
In this chapter we consider the computation of bases for the Krylov subspace \(\mathcal{K}_k(A,r_0)\). We could have used another notation for the vector on which the Krylov subspace is constructed, but in the next chapters, the Krylov subspaces we have to deal with will be based on the initial residual vector \(r_0=b-Ax_0\).
Gérard Meurant, Jurjen Duintjer Tebbens
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In this chapter we consider the computation of bases for the Krylov subspace \(\mathcal{K}_k(A,r_0)\). We could have used another notation for the vector on which the Krylov subspace is constructed, but in the next chapters, the Krylov subspaces we have to deal with will be based on the initial residual vector \(r_0=b-Ax_0\).
Gérard Meurant, Jurjen Duintjer Tebbens
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Analysis of Augmented Krylov Subspace Methods
SIAM Journal on Matrix Analysis and Applications, 1997``Augmented Krylov methods'' are studied theoretically. These methods for solving a linear system are projection methods in which the subspace of projection is of the form \(K = K_{m} + W\), where \(K_{m}\) is the standard Krylov subspace, which is augmented by another subspace \(W\). The subspace \(W\) can be chosen in different ways.
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