• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.127-143
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• 2015

In this paper, we consider a modified inexact Newton method for solving a nonlinear system F(x) = 0 where $F(x):R^n{\rightarrow}R^n$. The basic idea is to accelerate convergence. A semi-local convergence theorem for the modified inexact Newton method is established and an affine invariant version is also given. Moreover, we test three numerical examples which show that the modified inexact scheme is more efficient than the classical inexact Newton strategy.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.1
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• pp.91-107
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• 2002

This paper presents two new self-scaling variable-metric algorithms. The first is based on a known two-parameter family of rank-two updating formulae, the second employs an initial scaling of the estimated inverse Hessian which modifies the first self-scaling algorithm. The algorithms are compared with similar published algorithms, notably those due to Oren, Shanno and Phua, Biggs and with BFGS (the best known quasi-Newton method). The best of these new and published algorithms are also modified to employ inexact line searches with marginal effect. The new algorithms are superior, especially as the problem dimension increases.