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On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F20%3A00537319" target="_blank" >RIV/67985807:_____/20:00537319 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216208:11160/20:10417885

  • Result on the web

    <a href="http://dx.doi.org/10.1007/s11075-019-00846-z" target="_blank" >http://dx.doi.org/10.1007/s11075-019-00846-z</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s11075-019-00846-z" target="_blank" >10.1007/s11075-019-00846-z</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    On the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES

  • Original language description

    The paper gives a characterization of all linear systems such that when restarted GMRES is applied, prescribed admissible residual norms and (harmonic) Ritz values for all iterations inside the individual cycles are generated. Additionally, the system matrices can have any nonzero eigenvalues. The total number of GMRES iterations inside all cycles considered is assumed to be smaller than the system size. It is shown that stagnation at the end of a restart cycle must be mirrored at the beginning of the next cycle and that this is the only restriction for prescribed residual norms of restarted GMRES. The relation between prescribed residual norms of restarted GMRES and those of the corresponding full GMRES process is studied and linear systems are given where full and restarted GMRES give the same convergence history.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10102 - Applied mathematics

Result continuities

  • Project

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2020

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    Numerical Algorithms

  • ISSN

    1017-1398

  • e-ISSN

  • Volume of the periodical

    84

  • Issue of the periodical within the volume

    4

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    24

  • Pages from-to

    1329-1352

  • UT code for WoS article

    000547939900006

  • EID of the result in the Scopus database

    2-s2.0-85076567124