Convergence behaviour of inexact Newton methods

Benedetta Morini

doi:10.1090/s0025-5718-99-01135-7

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Convergence behaviour of inexact Newton methods

Benedetta Morini

Year: 1999 Journal: Mathematics of Computation Vol: 68 (228)Pages: 1605-1613 Publisher: American Mathematical Society

DOI: 10.1090/s0025-5718-99-01135-7

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Abstract

In this paper we investigate local convergence properties of inexact Newton and Newton-like methods for systems of nonlinear equations. Processes with modified relative residual control are considered, and new sufficient conditions for linear convergence in an arbitrary vector norm are provided. For a special case the results are affine invariant.

Keywords:

Mathematics Convergence (economics) Affine transformation Applied mathematics Residual Newton's method Norm (philosophy) Nonlinear system Local convergence Convergence tests Invariant (physics) Rate of convergence Mathematical optimization Iterative method Algorithm Computer science Pure mathematics

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Iterative Methods for Nonlinear Equations

Physical Sciences → Mathematics → Numerical Analysis

Advanced Optimization Algorithms Research

Physical Sciences → Mathematics → Numerical Analysis

Matrix Theory and Algorithms

Physical Sciences → Computer Science → Computational Theory and Mathematics

Convergence behaviour of inexact Newton methods

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