Relating computed and exact entities in methods based on Lanczos tridiagonalization
The result's identifiers
Result code in 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>
Alternative codes found
RIV/67985807:_____/18:00492190
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Relating computed and exact entities in methods based on Lanczos tridiagonalization
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GC17-04150J" target="_blank" >GC17-04150J: Reliable two-scale Fourier/finite element-based simulations: Error-control, model reduction, and stochastics</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Lecture Notes in Computer Science
ISBN
978-3-319-97135-3
ISSN
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e-ISSN
neuvedeno
Number of pages
15
Pages from-to
73-87
Publisher name
Springer Verlag
Place of publication
Switzerland
Event location
Karolinka, Czech Republic
Event date
May 22, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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