The evaluation of determinants by expansion by minors and the general problem of substitution

Gentleman, W. M.; Johnson, S. C.

doi:10.1090/S0025-5718-1974-0373369-7

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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The evaluation of determinants by expansion by minors and the general problem of substitution
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by W. M. Gentleman and S. C. Johnson PDF

Math. Comp. 28 (1974), 543-548 Request permission

Abstract:

In this paper, we consider a class of substitution strategies which correspond to various minor expansion algorithms, and show that the usual expansion by minors, a row at a time, is optimal in this class.

References

W. Morven Gentleman, Optimal multiplication chains for computing a power of a symbolic polynomial, Math. Comp. 26 (1972), 935–939. MR 314303, DOI 10.1090/S0025-5718-1972-0314303-3

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