Results 181 to 190 of about 78,319 (219)

Bases for Krylov subspaces

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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Projection Methods in Krylov Subspaces

Journal of Mathematical Sciences, 2019
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Spectral Variants of Krylov Subspace Methods

Numerical Algorithms, 2002
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Brígida Molina, Marcos Raydan
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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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Application of Krylov subspaces to SPECT imaging

International Journal of Imaging Systems and Technology, 2002
AbstractThe application of the conjugate gradient (CG) algorithm to the problem of data reconstruction in SPECT imaging indicates that most of the useful information is already contained in Krylov subspaces of small dimension, ranging from 9 (two‐dimensional case) to 15 (three‐dimensional case).
CALVINI P., BERTERO, MARIO
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On the Convergence of Restarted Krylov Subspace Methods

SIAM Journal on Matrix Analysis and Applications, 2000
The paper is concerned with investigation of convergence of Krylov subspace iterative method for the solution of large nonsymmetric linear systems. Restarted methods terminate the process after a fixed number of iterations and then repeat the procedure using the residual of the current approximate solution as new initial vector.
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Error-Minimizing Krylov Subspace Methods

SIAM Journal on Scientific Computing, 1994
This paper first introduces generalized conjugate gradient methods which specialize to error minimizing procedures as well as to residual minimizing methods. General minimum error methods are then introduced, and the two method classes are compared.
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Convergence Analysis of Restarted Krylov Subspace Eigensolvers

SIAM Journal on Matrix Analysis and Applications, 2016
Summary: The \(A\)-gradient minimization of the Rayleigh quotient allows one to construct robust and fast-convergent eigensolvers for the generalized eigenvalue problem for \((A,M)\) with symmetric and positive definite matrices. The \(A\)-gradient steepest descent iteration is the simplest case of more general restarted Krylov subspace iterations for ...
Klaus Neymeyr, Ming Zhou 0007
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Krylov Subspaces

2015
Voce di Enciclopedia. Abstract del libro: This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks
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Iterative Processes in the Krylov–Sonneveld Subspaces

Journal of Mathematical Sciences, 2017
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