English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Global and block Krylov subspace methods are efficient iterative solvers forlarge sparse linear systems with multiple right-hand sides. However, global orblock Lanczos-type solvers often exhibit large oscillations in the residualnorms and may have a large residual gap relating to the loss of attainableaccuracy of the approximations. Conventional residual smoothing schemessuppress these oscillations but cannot improve the attainable accuracy, whereasa recent residual smoothing scheme enables the improvement of the attainableaccuracy for single right-hand side Lanczos-type solvers. The underlyingconcept of this scheme is that the primary and smoothed sequences of theapproximations and residuals influence one another, thereby avoiding the severepropagation of rounding errors. In the present study, we extend thiscross-interactive residual smoothing to the case of solving linear systems withmultiple right-hand sides. The resulting smoothed methods can reduce theresidual gap with a low additional cost compared to their originalcounterparts. We demonstrate the effectiveness of the proposed approach throughrounding error analysis and numerical experiments.

Cross-interactive residual smoothing for global and block Lanczos-type solvers for linear systems with multiple right-hand sides