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ČeštinaEnglish

Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES

Result description

We show that arbitrary convergence behavior of Ritz values is possible in the Arnoldi method, and we give two parametrizations of the class of matrices with initial Arnoldi vectors that generate prescribed Ritz values (in all iterations). The second parametrization enables us to prove that any GMRES residual norm history is possible with any prescribed Ritz values (in all iterations), provided that we treat the stagnation case appropriately.

Keywords

Ritz valuesArnoldi processArnoldi methodGMRES methodprescribed convergenceinterlacing properties

The result's identifiers

Alternative languages

  • Result language

    angličtina

  • Original language name

    Any Ritz Value Behavior Is Possible for Arnoldi and for GMRES

  • Original language description

    We show that arbitrary convergence behavior of Ritz values is possible in the Arnoldi method, and we give two parametrizations of the class of matrices with initial Arnoldi vectors that generate prescribed Ritz values (in all iterations). The second parametrization enables us to prove that any GMRES residual norm history is possible with any prescribed Ritz values (in all iterations), provided that we treat the stagnation case appropriately.

  • Czech name

    —

  • Czech description

    —

Classification

  • Type

    Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

    —

Result continuities

Others

  • Publication year

    2012

  • Confidentiality

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

Data specific for result type

  • Name of the periodical

    SIAM Journal on Matrix Analysis and Applications

  • ISSN

    0895-4798

  • e-ISSN

    —

  • Volume of the periodical

    33

  • Issue of the periodical within the volume

    3

  • Country of publishing house

    US - UNITED STATES

  • Number of pages

    21

  • Pages from-to

    958-978

  • UT code for WoS article

    000310150300013

  • EID of the result in the Scopus database

    —

Basic information

Result type

Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

Jx

CEP

BA - General mathematics

Year of implementation

2012

Similar results(10)

Any Admissible Harmonic Ritz Value Set is Possible for GMRESPrescribing the behavior of early terminating GMRES and Arnoldi iterationsOn the residual norms, the Ritz values and the harmonic Ritz values that can be generated by restarted GMRES