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On investigating GMRES convergence using unitary matrices

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10281620" target="_blank" >RIV/00216208:11320/14:10281620 - isvavai.cz</a>

  • Alternative codes found

    RIV/67985807:_____/14:00427016 RIV/00216208:11160/14:10281620

  • Result on the web

    <a href="http://www.sciencedirect.com/science/article/pii/S0024379514001116" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0024379514001116</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1016/j.laa.2014.02.044" target="_blank" >10.1016/j.laa.2014.02.044</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On investigating GMRES convergence using unitary matrices

  • Original language description

    For a given matrix A and right-hand side b, this paper investigates unitary matrices generating, with some right-hand sides c, the same GMRES residual norms as the pair (A, b). We give characterizations of this class of unitary matrices and point out therelationship with Krylov subspaces and Krylov residual subspaces for the pair (A, b). We investigate the eigenvalues of these unitary matrices in relation to the convergence behavior of GMRES for the pair (A, b) and describe the indispensable role of the eigenvector information. We conclude with a formula for the GMRES residual norms generated by a normal matrix B in terms of its eigenvalues and components of the right-hand side c in the eigenvector basis.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2014

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Linear Algebra and Its Applications

  • ISSN

    0024-3795

  • e-ISSN

  • Volume of the periodical

    450

  • Issue of the periodical within the volume

    June

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    25

  • Pages from-to

    83-107

  • UT code for WoS article

    000336695700007

  • EID of the result in the Scopus database