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Conjugate direction methods for solving systems of linear equations

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Abstract

A generalization of the notion of a set of directions conjugate to a matrix is shown to lead to a variety of finitely terminating iterations for solving systems of linear equations. The errors in the iterates are characterized in terms of projectors constructable from the conjugate directions. The natural relations of the algorithms to well known matrix decompositions are pointed out. Some of the algorithms can be used to solve linear least squares problems.

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Authors and Affiliations

  1. Departments of Computer Science and of Mathematics Carnegie-Mellon University Pittsburgh, 15213, Pittsburgh, Pennsylvania, USA

    G. W. Stewart

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  1. G. W. Stewart
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Additional information

This work was supported by the Office of Naval Research under contract number N 00014-67-A-0126.

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Stewart, G.W. Conjugate direction methods for solving systems of linear equations. Numer. Math. 21, 285–297 (1973). https://doi.org/10.1007/BF01436383

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