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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Conditioning of quasi-Newton methods for function minimization
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by D. F. Shanno PDF
Math. Comp. 24 (1970), 647-656 Request permission

Abstract:

Quasi-Newton methods accelerate the steepest-descent technique for function minimization by using computational history to generate a sequence of approximations to the inverse of the Hessian matrix. This paper presents a class of approximating matrices as a function of a scalar parameter. The problem of optimal conditioning of these matrices under an appropriate norm as a function of the scalar parameter is investigated. A set of computational results verifies the superiority of the new methods arising from conditioning considerations to known methods.
References
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 647-656
  • MSC: Primary 90.58
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0274029-X
  • MathSciNet review: 0274029