Relating computed and exact entities in methods based on Lanczos tridiagonalization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384797" target="_blank" >RIV/00216208:11320/18:10384797 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/67985807:_____/18:00492190

Výsledek na webu

<a href="https://doi.org/10.1007/978-3-319-97136-0_6" target="_blank" >https://doi.org/10.1007/978-3-319-97136-0_6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-97136-0_6" target="_blank" >10.1007/978-3-319-97136-0_6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Relating computed and exact entities in methods based on Lanczos tridiagonalization

Popis výsledku v původním jazyce

Krylov subspace methods based on short recurrences such as CGL or MINRES represent an attractive way of solving large and sparse systems of linear algebraic equations. Loss of orthogonality in the underlying Lanczos process delays significantly their convergence in finite-precision computation, whose connection to exact computation is still not fully understood. In this paper, we exploit the idea of simultaneous comparison of finite-precision and exact computations for CGL and MINRES, by taking advantage of their relationship valid also in finite-precision arithmetic. In particular, we show that finite-precision CGL residuals and Lanczos vectors have to be aggregated over the intermediate iterations to form a counterpart to vectors from the exact computation. Influence of stagnation in exact MINRES computation is also discussed. Obtained results are supported by numerical experiments.

Název v anglickém jazyce

Relating computed and exact entities in methods based on Lanczos tridiagonalization

Popis výsledku anglicky

Krylov subspace methods based on short recurrences such as CGL or MINRES represent an attractive way of solving large and sparse systems of linear algebraic equations. Loss of orthogonality in the underlying Lanczos process delays significantly their convergence in finite-precision computation, whose connection to exact computation is still not fully understood. In this paper, we exploit the idea of simultaneous comparison of finite-precision and exact computations for CGL and MINRES, by taking advantage of their relationship valid also in finite-precision arithmetic. In particular, we show that finite-precision CGL residuals and Lanczos vectors have to be aggregated over the intermediate iterations to form a counterpart to vectors from the exact computation. Influence of stagnation in exact MINRES computation is also discussed. Obtained results are supported by numerical experiments.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GC17-04150J" target="_blank" >GC17-04150J: Robustní dvojúrovňové simulace založené na Fourierově metodě a metodě konečných prvků: Odhady chyb, redukované modely a stochastika</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Lecture Notes in Computer Science

ISBN

978-3-319-97135-3

ISSN

—

e-ISSN

neuvedeno

Počet stran výsledku

15

Strana od-do

73-87

Název nakladatele

Springer Verlag

Místo vydání

Switzerland

Místo konání akce

Karolinka, Czech Republic

Datum konání akce

22. 5. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—