Number of the records: 1
Preconditioning of two-by-two block matrix systems with square matrix blocks, with applications
- 1.
SYSNO ASEP 0482832 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Preconditioning of two-by-two block matrix systems with square matrix blocks, with applications Author(s) Axelsson, Owe (UGN-S) RID Number of authors 1 Source Title Applications of Mathematics. - : Springer - ISSN 0862-7940
Roč. 62, č. 6 (2017), s. 537-559Number of pages 23 s. Publication form Online - E Action SNA´17 - Seminar on numerical analysis Event date 30.01.2017 - 03.02.2017 VEvent location Ostrava Country CZ - Czech Republic Event type CST Language eng - English Country CZ - Czech Republic Keywords preconditioning ; Schur complement ; transformation ; optimal control ; implicit time integration Subject RIV BA - General Mathematics OECD category Applied mathematics Institutional support UGN-S - RVO:68145535 UT WOS 000419946700002 DOI 10.21136/AM.2017.0222-17 Annotation Two-by-two block matrices of special form with square matrix blocks arise in important applications, such as in optimal control of partial differential equations and in high order time integration methods. Two solution methods involving very efficient preconditioned matrices, one based on a Schur complement reduction of the given system and one based on a transformation matrix with a perturbation of one of the given matrix blocks are presented. The first method involves an additional inner solution with the pivot matrix block but gives a very tight condition number bound when applied for a time integration method. The second method does not involve this matrix block but only inner solutions with a linear combination of the pivot block and the off-diagonal matrix blocks. Both the methods give small condition number bounds that hold uniformly in all parameters involved in the problem, i.e. are fully robust. The paper presents shorter proofs, extended and new results compared to earlier publications. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2018 Electronic address http://articles.math.cas.cz/10.21136/AM.2017.0222-17/?type=F
Number of the records: 1