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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.


A quasi-Newton method with no derivatives
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by John Greenstadt PDF
Math. Comp. 26 (1972), 145-166 Request permission


The Davidon formula and others of the “quasi-Newton” class, which are used in the unconstrained minimization of a function $f$, provide a (generally) convergent sequence of approximations to the Hessian of $f$. These formulas, however, require the independent calculation of the gradient of $f$. In this paper, a set of new formulas is derived—using a previously described variational approach—which successively approximates the gradient as well as the Hessian, and uses only function values. These formulas are incorporated into an algorithm which, although still crude, works quite well for various standard test functions. Extensive numerical results are presented.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 145-166
  • MSC: Primary 65K05
  • DOI:
  • MathSciNet review: 0305592