ISSN:
1572-9125
Keywords:
15A06
;
65F05
;
65F10
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Linear systems with a fairly well-conditioned matrixM of the form $$\begin{array}{*{20}c} n \\ 1 \\ \end{array} \mathop {\left( {\begin{array}{*{20}c} A & b \\ c & d \\ \end{array} } \right)}\limits^{\begin{array}{*{20}c} n & 1 \\ \end{array} } $$ , for which a ‘black box’ solver forA is available, can be accurately solved by the standard process of Block Elimination, followed by just one step of Iterative Refinement, no matter how singularA may be — provided the ‘black box’ has a property that is possessed by LU- and QR-based solvers with very high probability. The resulting Algorithm BE + 1 is simpler and slightly faster than T.F. Chan's Deflation Method, and just as accurate. We analyse the case where the ‘black box’ is a solver not forA but for a matrix close toA. This is of interest for numerical continuation methods.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01931663
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