Skip to Main content Skip to Navigation
New interface
Reports (Research report)

A block minimum residual norm subspace solver for sequences of multiple left and right-hand side linear systems

Abstract : We are concerned with the iterative solution of linear systems with multiple right-hand sides available one group after another, including the case where there are massive number (like tens of thousands) of right-hand sides associated with a single matrix so that all of them cannot be solved at once but rather need to be split into chunks of possible variable sizes. For such sequences of linear systems with multiple leftand right-hand sides, we develop a new recycling block generalized conjugate residual method with inner orthogonalization and inexact breakdown (IB-BGCRO-DR), which glues subspace recycling technique in GCRO-DR [SIAM J. Sci. Comput., 28(5) (2006), pp. 1651–1674] and inexact breakdown mechanism in IB-BGMRES [Linear Algebra Appl., 419 (2006), pp. 265–285] to guarantee this new algorithm could reuse spectral information for subsequent cycles as well as for the remaining linear systems to be solved. Related variant IB-BFGCRO-DR that suits for flexible preconditioning is devised to cope with constraints on some applications while also enabling mixed-precision calculation, which provides advantages in speed and memory usage over double precision as well as in perspective of emerging computing units such as the GPUs.
Complete list of metadata

https://hal.inria.fr/hal-03146213
Contributor : Luc Giraud Connect in order to contact the contributor
Submitted on : Tuesday, October 12, 2021 - 10:06:23 PM
Last modification on : Wednesday, October 26, 2022 - 8:15:48 AM

File

RR-9393.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-03146213, version 3

Citation

Luc Giraud, Yan-Fei Jing, Yanfei Xiang. A block minimum residual norm subspace solver for sequences of multiple left and right-hand side linear systems. [Research Report] RR-9393, Inria Bordeaux Sud-Ouest. 2021, pp.60. ⟨hal-03146213v3⟩

Share

Metrics

Record views

266

Files downloads

230