A new family of global methods for linear systems with multiple right-hand sides
Jianhua Zhang,Hua Dai,Jing Zhao +2 more
TLDR
In this paper, a new family of global A -biorthogonal methods by using short two-term recurrences and formal orthogonal polynomials, which contain the global bi-conjugate residual (Gl-BCR) algorithm and its improved version, was presented.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2011-10-01 and is currently open access. It has received 22 citations till now. The article focuses on the topics: Krylov subspace & Linear system.read more
Citations
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Block Krylov subspace methods for functions of matrices
TL;DR: A class of efficient block Krylov subspace methods tailored precisely to the evaluation of a matrix function on not just one but multiple vectors is developed, demonstrating the power and versatility of this new class of methods for a variety of matrix-valued inner products, functions, and matrices.
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A breakdown-free block conjugate gradient method
Hao Ji,Yaohang Li +1 more
TL;DR: A simple solution, breakdown-free block conjugate gradient (BFBCG), is designed to address the rank deficiency problem, and the rationale of the BFBCG algorithm is to derive new forms of parameter matrices based on the potentially reduced search subspace to handle rank deficiency.
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Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM
TL;DR: An expansion of the generalized block Krylov subspace framework of [Electron. Anal., 47 (2017), pp. 100--126] allows the use of low-rank modifications of the Krylovsubspace framework.
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The block CMRH method for solving nonsymmetric linear systems with multiple right-hand sides
TL;DR: A block version of the CMRH algorithm for solving linear systems with multiple right-hand sides is presented and it is shown that under the condition of full rank of block residual the block C MRH method cannot break down.
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On short recurrence Krylov type methods for linear systems with many right-hand sides
TL;DR: In this paper, the authors consider the most established Krylov subspace methods which rely on short recurrences and propose modifications of their block variants which increase numerical stability, thus at least partly curing a problem previously observed by several authors.
References
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An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix
TL;DR: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed, if the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm.
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The block conjugate gradient algorithm and related methods
TL;DR: A block biconjugate gradient algorithm for general matrices is developed, and block conjugate gradient, minimum residual, and minimum error algorithms for symmetric semidefinite matrices are developed.
Journal ArticleDOI
Variants of BICGSTAB for matrices with complex spectrum
TL;DR: The author presents for real nonsymmetric matrices a method BICGSTAB2 in which the second factor may have complex conjugate zeros, and versions suitable for complex matrices are given for both methods.
Journal ArticleDOI
Global FOM and GMRES algorithms for matrix equations
TL;DR: New methods for solving nonsymmetric linear systems of equations with multiple right-hand sides based on global oblique and orthogonal projections of the initial matrix residual onto a matrix Krylov subspace are presented.
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A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides
Roland W. Freund,Manish Malhotra +1 more
TL;DR: A block version of Freund and Nachtigal's quasi-minimal residual (QMR) method for the iterative solution of non-Hermitian linear systems is proposed and shown how to incorporate deflation to drop converged linear systems, and to delete linearly and almost linearly dependent vectors in the underlying block Krylov sequences.
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Global FOM and GMRES algorithms for matrix equations
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