Projected Krylov methods for saddle-point systems

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Persistent URL	http://purl.org/net/epubs/work/65298
Record Status	Checked
Record Id	65298
Title	Projected Krylov methods for saddle-point systems
Contributors	NIM Gould (STFC Rutherford Appleton Lab.), D Orban, T Rees (STFC Rutherford Appleton Lab.)
Abstract	Projected Krylov methods are full-space formulations of Krylov methods that take place in a nullspace. Provided projections into the nullspace can be computed accurately, those methods only require products between an operator and vectors lying in the nullspace. In the symmetric case, their convergence is thus entirely described by the spectrum of the (preconditioned) operator restricted to the nullspace. We provide systematic principles for obtaining the projected form of any well-de ned Krylov method. Equivalence properties between projected Krylov methods and standard Krylov methods applied to a saddle-point operator with a constraint preconditioner allow us to show that, contrary to common belief, certain known methods such as MINRES and SYMMLQ are well de ned in the presence of an inde nite preconditioner.
Organisation	STFC , SCI-COMP , SCI-COMP-CM
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Report	RAL Preprints RAL-P-2013-006. 2013.		RAL-P-2013-006.pdf	2013