Abstract

The role of Broyden′s method as a powerful quasi‐Newton method for solving unconstrained optimization problems or a system of nonlinear algebraic equations is well known. We offer here a general convergence criterion for a method akin to Broyden′s method in Rn. The approach is different from those of other convergence proofs which are available only for the direct prediction methods.

Highlights

  • The role of Broyden’s method as a powerful quasi-Newton method for solving unconstrained optimization problems or a system of nonlinear algebraic equations is well known

  • V--- T Our concern in this paper is iteratlve n methods for the solution of simultaneous non-llnear equations

  • The convergence results that are available to date are proved for the direct prediction method [5]

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Summary

The algorithm under consideration takes the form

(1 where H n is generated by the method in such a way that the quasi-Newton equation.

Rm such that
If bij
Pn ss Writing sn taken as
Then starting from x o
Bn Xn Using the fact that is an
Continuity of F yields that
Therefore for xD
If SkHkYk
We take t x
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