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Original Articles

Numerical solution of 2 × 2 block linear systems by block Gram–Schmidt methods

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Pages 1562-1573 | Received 02 Dec 2013, Accepted 13 Apr 2016, Published online: 03 Sep 2016
 

ABSTRACT

In this paper we propose and analyse some algorithms for solving 2×2 block linear systems which are based upon the block Gram–Schmidt method. In particular, we prove that the algorithm BCGS2 (Reorthogonalized Block Classical Gram–Schmidt) using Householder Q–R decomposition implemented in floating-point arithmetic is backward stable, under the mild assumptions. Numerical tests were done in MATLAB to illustrate our theoretical results. A particular emphasis is on symmetric saddle-point problems, which arise in many important practical applications. We compare the results with the generalized minimal residual (GMRES) algorithm.

2010 AMS SUBJECT CLASSIFICATIONS:

Acknowledgements

The authors are grateful to the referees for the many suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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