The block Lanczos method for linear systems with multiple right-hand sides

Guennouni, A. El; Jbilou, Khalide; Sadok, H.

doi:10.1016/j.apnum.2004.04.001

Cited by 77 publications

(93 citation statements)

References 26 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Um avanço mais recente que será apresentado na seção 5.4, está relacionado a se permitir que o produto matriz-vetor seja calculado de forma inexata, necessidade sentida em áreas aonde a matriz não é disponível ou é muito cara para ser calculada exatamente ( [19], [20], [52], [112], [114], [129]). Apresentamos, a seguir, uma bibliografia onde as várias propostas aqui discutidas, e outras que não trataremos, podem ser estudadas: [9], [22], [25], [26], [34], [37], [49], [62], [63], [77], [89], [95], [100], [109] e [140]. [86]), em um grande número de problemas importantes, a convergên-cia dos MPSK depende em larga escala da distribuição dos autovalores.…”

Section: Novos Desenvolvimentos Dos Métodos De Krylovunclassified

Avanços em Métodos de Krylov para Solução de Sistemas Lineares de Grande Porte

2009

Notas Em Matemática Aplicada

View full text Add to dashboard Cite

Section: Novos Desenvolvimentos Dos Métodos De Krylovunclassified

Avanços em Métodos de Krylov para Solução de Sistemas Lineares de Grande Porte

2009

Notas Em Matemática Aplicada

View full text Add to dashboard Cite

“…Generally, block Krylov methods are more efficient when they are applied to relatively dense linear systems and combined with some preconditioning techniques [9]. In this first class, one can cite the block conjugate gradient (Bl-CG) for symmetric definite matrices, the block Bi-conjugate Gradient (Bl-BCG) and the block Bi-Conjugate Gradient stabilized (Bl-BiCGSTAB) methods [4,16]. Other popular methods can be enumerated like the block-quasi-minimal residual (Bl-QMR) algorithm [5,14], the block-generalized minimum residual (Bl-GMRES) algorithm [20,22].…”

Section: Introductionmentioning

confidence: 99%

On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems

Elbouyahyaoui¹,

Heyouni

2018

B Soc Paran Mat

View full text Add to dashboard Cite

In the present paper, we are concerned by weighted Arnoldi like methods for solving large and sparse linear systems that have different right-hand sides but have the same coefficient matrix. We first give detailed descriptions of the weighted Gram-Schmidt process and of a Ruhe variant of the weighted block Arnoldi algorithm. We also establish some theoretical results that links the iterates of the weighted block Arnoldi process to those of the non weighted one. Then, to accelerate the convergence of the classical restarted block and seed GMRES methods, we introduce the weighted restarted block and seed GMRES methods. Numerical experiments are reported at the end of this work in order to compare the performance and show the effectiveness of the proposed methods.

show abstract

“…Since the Dirac matrix in lattice QCD is nonHermitian, we might expect the block BiCGSTAB algorithm [3] is applicable in a straightforward way. One problem in block Krylov subspace methods, however, is that the true residual stops decreasing at some point, while the recursive one continues to decrease.…”

Section: Introductionmentioning

confidence: 99%

Modified block BiCGSTAB for lattice QCD

Nakamura¹,

Ishikawa²,

Kuramashi³

et al. 2012

Computer Physics Communications

View full text Add to dashboard Cite

We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD on a 32 3 × 64 lattice at almost physical quark masses. The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one. The SAP preconditioner applied to the domain-decomposed lattice helps us minimize communication overhead. We find remarkable cost reduction thanks to cache tuning and reduction of number of iterations.

show abstract

The block Lanczos method for linear systems with multiple right-hand sides

Cited by 77 publications

References 26 publications

Avanços em Métodos de Krylov para Solução de Sistemas Lineares de Grande Porte

Avanços em Métodos de Krylov para Solução de Sistemas Lineares de Grande Porte

On applying weighted seed techniques to GMRES algorithm for solving multiple linear systems

Modified block BiCGSTAB for lattice QCD

Contact Info

Product

Resources

About