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The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity

Keller, Herbert B. (1983) The Bordering Algorithm and Path Following Near Singular Points of Higher Nullity. SIAM Journal on Scientific and Statistical Computing, 4 (4). pp. 573-582. ISSN 0196-5204. doi:10.1137/0904039.

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We study the behavior of the bordering algorithm (a form of block elimination) for solving nonsingular linear systems with coefficient matrices in the partitioned form (A & B \\ C^* & D) when N(A)≧1. Systems with this structure naturally occur in path following procedures. We show that under appropriate assumptions, the algorithm, which is based on solving systems with coefficient matrix A, works as A varies along a path and goes through singular points. The required assumptions are justified for a large class of problems coming from discretizations of boundary value problems for differential equations.

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Additional Information:© 1983 Society for Industrial and Applied Mathematics. Received by the editors March 15, 1982, and in revised form July 26, 1982. This work was supported by the U.S. Department of Energy under contract EY-76-S-03-0767, Project agreement #12, and the U.S. Army Research Office under contract DAAG 29-78-C-0011. I wish to thank the referees for helpful comments on the original version of this paper.
Funding AgencyGrant Number
Department of Energy (DOE)EY-76-S-03-0767
Army Research Office (ARO)DAAG 29-78-C-0011
Subject Keywords:path following; bordering algorithm; block elimination; singular systems
Issue or Number:4
Record Number:CaltechAUTHORS:20120712-141249734
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:32395
Deposited On:12 Jul 2012 21:35
Last Modified:09 Nov 2021 21:27

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