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%2F67985807%3A_____%2F20%3A00525243" target="_blank" >RIV/67985807:_____/20:00525243 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24220/20:00007782
Result on the web
<a href="https://www.anstuocmath.ro/volume-xxviii-2020-fascicola-2.html" target="_blank" >https://www.anstuocmath.ro/volume-xxviii-2020-fascicola-2.html</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
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA17-12925S" target="_blank" >GA17-12925S: Strength of materials and mechanical components based on iron: Multi-scale approach</a><br>
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
Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica
ISSN
1224-1784
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