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.
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- © 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