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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

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • 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

  • 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