A note on constraint preconditioning

Daniel Loghin

doi:10.1137/16M1072036

A note on constraint preconditioning

Daniel Loghin

Mathematics

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2 Citations (Scopus)

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Abstract

We discuss and extend the results derived in Keller, Gould and Wathen [SIMAX, 21(4), 2000] for constraint preconditioning. In particular, we improve the existing results as well as generalise them to the case where the (1,1) block of the preconditioner has a non-trivial kernel. We also analyse the form of the preconditioner with negated constraints, which ensures that the preconditioned system is diagonalisable, while preserving the non-unit eigenvalues and negating some unit eigenvalues.

Original language	English
Pages (from-to)	1486–1495
Number of pages	10
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	38
Issue number	4
Early online date	6 Dec 2017
DOIs	https://doi.org/10.1137/16M1072036
Publication status	E-pub ahead of print - 6 Dec 2017

Keywords

constraint preconditioning
Krylov subspace methods
saddle-point problems

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10.1137/16M1072036

Loghin_A_note_on_constraint_preconditioning_SIAM_Journal_on_Matrix_Analysis_and_Applications_2017
© 2016, Society for Industrial and Applied Mathematics Accepted for publication in SIAM Journal on Matrix Analysis and Applications, published in December 2017 at: https://doi.org/10.1137/16M1072036
Accepted author manuscript, 234 KBLicence: Other (please specify with Rights Statement)

Cite this

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AB - We discuss and extend the results derived in Keller, Gould and Wathen [SIMAX, 21(4), 2000] for constraint preconditioning. In particular, we improve the existing results as well as generalise them to the case where the (1,1) block of the preconditioner has a non-trivial kernel. We also analyse the form of the preconditioner with negated constraints, which ensures that the preconditioned system is diagonalisable, while preserving the non-unit eigenvalues and negating some unit eigenvalues.

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KW - Krylov subspace methods

KW - saddle-point problems

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A note on constraint preconditioning

Abstract

Keywords

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