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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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.

 

Optimal conditioning of quasi-Newton methods
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by D. F. Shanno and P. C. Kettler PDF
Math. Comp. 24 (1970), 657-664 Request permission

Abstract:

Quasi-Newton methods accelerate gradient methods for minimizing a function by approximating the inverse Hessian matrix of the function. Several papers in recent literature have dealt with the generation of classes of approximating matrices as a function of a scalar parameter. This paper derives necessary and sufficient conditions on the range of one such parameter to guarantee stability of the method. It further shows that the parameter effects only the length, not the direction, of the search vector at each step, and uses this result to derive several computational algorithms. The algorithms are evaluated on a series of test problems.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 657-664
  • MSC: Primary 90.58
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0274030-6
  • MathSciNet review: 0274030