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Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks
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SYSNO ASEP 0534464 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Superior properties of the PRESB preconditioner for operators on two-by-two block form with square blocks Tvůrce(i) Axelsson, Owe (UGN-S) RID
Karátson, J. (HU)Celkový počet autorů 2 Zdroj.dok. Numerische Mathematik - ISSN 0029-599X
Roč. 146, č. 2 (2020), s. 335-368Poč.str. 34 s. Forma vydání Online - E Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova preconditioner ; PRESB method ; superlinear convergence Vědní obor RIV BA - Obecná matematika Obor OECD Applied mathematics CEP LQ1602 GA MŠMT - Ministerstvo školství, mládeže a tělovýchovy Způsob publikování Open access Institucionální podpora UGN-S - RVO:68145535 UT WOS 000563156700001 EID SCOPUS 85089871065 DOI 10.1007/s00211-020-01143-x Anotace Matrices or operators in two-by-two block form with square blocks arise in numerous important applications, such as in optimal control problems for PDEs. The problems are normally of very large scale so iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is of crucial importance. Since some time a very efficient preconditioner, the preconditioned square block, PRESB method has been used by the authors and coauthors in various applications, in particular for optimal control problems for PDEs. It has been shown to have excellent properties,
such as a very fast and robust rate of convergence that outperforms other methods. In this paper the fundamental and most important properties of the method are stressed and presented with new and extended proofs. Under certain conditions, the condition number of the preconditioned matrix is bounded by 2 or even smaller. Furthermore, under certain assumptions the rate of convergence is superlinear.Pracoviště Ústav geoniky Kontakt Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Rok sběru 2021 Elektronická adresa https://link.springer.com/article/10.1007%2Fs00211-020-01143-x
Počet záznamů: 1