A New Projected Variant of the Deflated Block Conjugate Gradient Method

Xiang, Yanfei; Jing, Yan-Fei; Huang, Ting‐Zhu

doi:10.1007/s10915-019-00969-4

J Sci Comput

2019

DOI: 10.1007/s10915-019-00969-4

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A New Projected Variant of the Deflated Block Conjugate Gradient Method

Yanfei Xiang

Yan-Fei Jing

Ting‐Zhu Huang

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Cited by 4 publications

(1 citation statement)

References 33 publications

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“…For the sake of balancing robustness and convergence rate, Robbé and Sadkane proposed an inexact breakdown detection for the block GMRES algorithm (denoted by IB-BGMRES) [20], which could keep and reintroduce directions associated with the almost converged parts in next iteration if necessary. We refer to [1,2,20], for relevant works on inexact breakdown detection, as well as to [23][24][25][26]28], for related variants of block Krylov subspace methods for solving linear systems with multiple right-hand sides.…”

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confidence: 99%

A Block Minimum Residual Norm Subspace Solver with Partial Convergence Management for Sequences of Linear Systems

Giraud¹,

Jing²,

Xiang³

2022

SIAM J. Matrix Anal. Appl.

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We are concerned with the iterative solution of linear systems with multiple right-hand sides available one group after another with possibly slowly-varying left-hand sides. For such sequences of linear systems, we first develop a new block minimum norm residual approach that combines two main ingredients. The first component exploits ideas from GCRO-DR [SIAM J. Sci. Comput., 28(5) (2006), pp. 1651-1674, enabling to recycle information from one solve to the next. The second component is the numerical mechanism to manage the partial convergence of the right-hand sides, referred to as inexact breakdown detection in IB-BGMRES [Linear Algebra Appl., 419 (2006), pp. 265-285], that enables the monitoring of the rank deficiency in the residual space basis expanded block-wise.Secondly, for the class of block minimum norm residual approaches, that relies on a block Arnoldi-like equality between the search space and the residual space (e.g., any block GMRES or block GCRO variants), we introduce new search space expansion policies defined on novel criteria to detect the partial convergence. These novel detection criteria are tuned to the selected stopping criterion and targeted convergence threshold to best cope with the selected normwise backward error stopping criterion, enabling to monitor the computational effort while ensuring the final accuracy of each individual solution. Numerical experiments are reported to illustrate the numerical and computational features of both the new block Krylov solvers and the new search space block expansion polices.

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confidence: 99%

A Block Minimum Residual Norm Subspace Solver with Partial Convergence Management for Sequences of Linear Systems

Giraud¹,

Jing²,

Xiang³

2022

SIAM J. Matrix Anal. Appl.

Self Cite

View full text Add to dashboard Cite

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Two New Variants of the Simpler Block GMRES Method with Vector Deflation and Eigenvalue Deflation for Multiple Linear Systems

Tajaddini

Saberi-Movahed

et al. 2021

J Sci Comput

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Low-rank tensor completion via combined non-local self-similarity and low-rank regularization

Zhao

Jiang

et al. 2019

Neurocomputing

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A New Projected Variant of the Deflated Block Conjugate Gradient Method

Cited by 4 publications

References 33 publications

A Block Minimum Residual Norm Subspace Solver with Partial Convergence Management for Sequences of Linear Systems

A Block Minimum Residual Norm Subspace Solver with Partial Convergence Management for Sequences of Linear Systems

Two New Variants of the Simpler Block GMRES Method with Vector Deflation and Eigenvalue Deflation for Multiple Linear Systems

Low-rank tensor completion via combined non-local self-similarity and low-rank regularization

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