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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

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


Authors: W. M. Gentleman and S. C. Johnson
Journal: Math. Comp. 28 (1974), 543-548
MSC: Primary 68A20
MathSciNet review: 0373369
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] W. M. Gentleman, "Optimal multiplication chains for computing a power of a symbolic polynomial," Math Comp., v. 26, 1972, pp. 935-939. MR 0314303 (47:2855)
  • [2] Sir Thomas Muir, The Theory of Determinants in the Historical Order of Development, Macmillan, London, 1906-1920.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0373369-7
PII: S 0025-5718(1974)0373369-7
Keywords: Substitution, expansion by minors, determinants
Article copyright: © Copyright 1974 American Mathematical Society