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DOI 10.5286/raltr.2009015
Persistent URL http://purl.org/net/epubs/work/51038
Record Status Checked
Record Id 51038
Title Partial factorization of a dense symmetric indefinite matrix
Abstract At the heart of a frontal or multifuntional solver for the solution of sparse symmetric sets of linear equations, there is the need to partially factorize dense matrices (the frontal matrices) and to be able to use their factorizations in subsequent forward and backward substitutions. For a large problem, packing (holding only the lower or upper triangle part) is imoortant to save memory. It has long been recognised that blocking is the key to efficiency and this has become partially relevant on modern hardware. For stability in the indefinite case, the use of interchanges and 2x2 pivots as well as 1x1 pivots is equally well established. It is shown here that it is possible to use these ideas together to achieve stable factorizations of large real-world problems with good execution speed. The ideas are not restricted to frontal and multifrontal solvers and are aplicable whenever partial or complete factorizations of dense symmetric indefinite matrices are needed.
Organisation CSE , CSE-NAG , STFC
Keywords frontal , 2x2 pivots , sparse symmetric linear systems , multifrontal , interchanges , LDL(superscript)T factorization
Funding Information
Related Research Object(s): 49217593
Licence Information:
Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2009-015. STFC, 2009. rsRAL2009015.pdf 2009