Matrix analysis
Designing efficient algorithms for parallel computers
Designing efficient algorithms for parallel computers
Asymptotic mesh independence of Newton-Galerkin methods via a refined Mysovskii theorem
SIAM Journal on Numerical Analysis
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
The two-stage arithmetic mean method
Applied Mathematics and Computation
Convergence behaviour of inexact Newton methods
Mathematics of Computation
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Computer Architecture and Parallel Processing
Computer Architecture and Parallel Processing
Numerical Analysis: A First Course in Scientific Computation
Numerical Analysis: A First Course in Scientific Computation
Implementation of splitting methods for solving block tridiagonal linear systems on transputers
PDP '95 Proceedings of the 3rd Euromicro Workshop on Parallel and Distributed Processing
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Convergence behaviour of inexact Newton methods under weak Lipschitz condition
Journal of Computational and Applied Mathematics
Inner solvers for interior point methods for large scale nonlinear programming
Computational Optimization and Applications
On solving a special class of weakly nonlinear finite-difference systems
International Journal of Computer Mathematics
Convergence behaviour of inexact Newton methods under weak Lipschitz condition
Journal of Computational and Applied Mathematics
| Hi-index | 0.48 |
This paper is concerned with the development of the Newton-arithmetic mean method for large systems of nonlinear equations with block-partitioned Jacobian matrix. This method is well suited for implementation on a parallel computer; its degree of decomposition is very high. The convergence of the method is analysed for the class of systems whose Jacobian matrix satisfies an affine invariant Lipschitz condition. An estimation of the radius of the attraction ball is given. Special attention is reserved to the case of weakly nonlinear systems. A numerical example highlights some peculiar properties of the method.