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A note on adaptivity in factorized approximate inverse preconditioning

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10421701" target="_blank" >RIV/00216208:11320/20:10421701 - isvavai.cz</a>

  • Result on the web

    <a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ToOIwIS_1j" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=ToOIwIS_1j</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.2478/auom-2020-0024" target="_blank" >10.2478/auom-2020-0024</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    A note on adaptivity in factorized approximate inverse preconditioning

  • Original language description

    The problem of solving large-scale systems of linear algebraic equations arises in a wide range of applications. In many cases the preconditioned iterative method is a method of choice. This paper deals with the approximate inverse preconditioning AINV/SAINV based on the incomplete generalized Gram-Schmidt process. This type of the approximate inverse preconditioning has been repeatedly used for matrix diagonalization in computation of electronic structures but approximating inverses is of an interest in parallel computations in general. Our approach uses adaptive dropping of the matrix entries with the control based on the computed intermediate quantities. Strategy has been introduced as a way to solve difficult application problems and it is motivated by recent theoretical results on the loss of orthogonality in the generalized Gram-Schmidt process. Nevertheless, there are more aspects of the approach that need to be better understood. The diagonal pivoting based on a rough estimation of condition numbers of leading principal submatrices can sometimes provide inefficient preconditioners. This short study proposes another type of pivoting, namely the pivoting that exploits incremental condition estimation based on monitoring both direct and inverse factors of the approximate factorization. Such pivoting remains rather cheap and it can provide in many cases more reliable preconditioner. Numerical examples from real-world problems, small enough to enable a full analysis, are used to illustrate the potential gains of the new approach.

  • 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

    <a href="/en/project/GA18-12719S" target="_blank" >GA18-12719S: Thermodynamical and mathematical analysis of flows of complex fluids</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

    Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica [online]

  • ISSN

    1844-0835

  • e-ISSN

  • Volume of the periodical

    28

  • Issue of the periodical within the volume

    2

  • Country of publishing house

    RO - ROMANIA

  • Number of pages

    11

  • Pages from-to

    149-159

  • UT code for WoS article

    000574556300009

  • EID of the result in the Scopus database

    2-s2.0-85093503628