Monotone discrete Newton iterations and elimination
type: Item
instance of: scholarly article
title: Monotone discrete Newton iterations and elimination
zbMATH Open document ID: 0842.65030
DOI: 10.1016/0898-1221(95)00069-B
publication date: 1996-08-05T00:00:00Z
review text: The paper studies the Newton method for the solution of nonlinear algebraic systems with a Jacobian which is an M-matrix. For this case, it is well known that with two properly choosen starting guesses it is possible to obtain two monotone sequences of the Newton iterations which approach the exact solution quadratically and componentwise from below and from above, respectively. These results are extended to the case of the discrete Newton method using a finite difference approximation of the Jacobian. It is also shown that the quadratic convergence can be achieved in this case if the stepsize for the approximation of the Jacobian goes to zero. All these properties are studied once again in the case when some unknowns are eliminated directly from the nonlinear system. Numerical experiments illustrate the theoretical results and show a suitable choice of the stepsize for the discrete Newton method.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 825384
zbMATH Keywords: monotone Newton iterations
zbMATH Keywords: numerical experiments
zbMATH Keywords: nonlinear algebraic systems
zbMATH Keywords: quadratic convergence
zbMATH Keywords: discrete Newton method
author: Juan Pedro Milaszewicz
reviewed by: R. Blaheta
MaRDI profile type: Publication
cites work: Q5652137
cites work: Improving Jacobi and Gauss-Seidel iterations
cites work: Elimination and fixed point iterations
cites work: Q4060241
cites work: Q5809521
cites work: Monotone Iterations for Nonlinear Equations with Application to Gauss-Seidel Methods
cites work: Comparison theorems for monotone Newton-Fourier iterations and applications in functional elimination
cites work: Errata to: ``Elimination and fixed point iterations''
full work available at URL: 0898-1221(95)00069-b
OpenAlex ID: W1967647958
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 825384