A null-space approach for symmetric saddle point systems with a non zero (2,2) block

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Persistent URL	http://purl.org/net/epubs/work/46693872
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Record Id	46693872
Title	A null-space approach for symmetric saddle point systems with a non zero (2,2) block
Contributors	J Scott (STFC Rutherford Appleton Lab.), M Tuma
Abstract	Null-space methods have long been used to solve large-scale symmetric saddle point systems of equations in which the k k (2; 2) block is zero. This paper focuses on the case where the (2; 2) block is non zero. A novel null-space approach is proposed to transform the saddle point system into another symmetric saddle point system of the same order but with a zero (2; 2) block of order at most 2k. Success of any null-space approach is dependent on the construction of a suitable null-space basis. The not uncommon case of the off-diagonal block being a wide matrix that has far fewer rows than columns and that may be dense is considered. A number of approaches are explored with the aim of balancing stability of the transformed system with sparsity. Linear least squares problems that contain a small number of dense rows arising from practical applications are used to illustrate our ideas and to explore their potential for solving large-scale systems.
Organisation	STFC , SCI-COMP
Keywords
Funding Information
Related Research Object(s):	51321318
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Language	English (EN)

Type	Details	URI(s)	Local file(s)	Year
Preprint	RAL Preprints RAL-P-2020-003, SIAM J Sci Comput STFC, 2020.		RAL-P-2020-003 .pdf	2020