The Newton-arithmetic mean method for the solution of systems of nonlinear equations.

DOI10.1016/S0096-3003(01)00265-XzbMath1047.65031MaRDI QIDQ1855914

Emanuele Galligani

Publication date: 28 January 2003

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

convergencenumerical experimentsparallel computationaffine invariancesemi-linear elliptic systemweakly nonlinear systemsarithmetic mean methodlarge systems of nonlinear equationsNewton-iterative method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Parallel numerical computation (65Y05) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (12)

SSOR and ASSOR preconditioners for block-Broyden method ⋮ Inner solvers for interior point methods for large scale nonlinear programming ⋮ On CSCS-based iteration methods for Toeplitz system of weakly nonlinear equations ⋮ A class of iteration methods based on the generalized preconditioned Hermitian and skew-Hermitian splitting for weakly nonlinear systems ⋮ A class of iteration methods based on the HSS for Toeplitz systems of weakly nonlinear equations ⋮ Lagged diffusivity fixed point iteration for solving steady-state reaction diffusion problems ⋮ The arithmetic mean method for solving systems of nonlinear equations in finite differences ⋮ Inexact block Newton methods for solving nonlinear equations ⋮ Convergence behaviour of inexact Newton methods under weak Lipschitz condition. ⋮ On LPMHSS-based iteration methods for a class of weakly nonlinear systems ⋮ On solving a special class of weakly nonlinear finite-difference systems ⋮ Performance analysis of Arithmetic Mean method for solving composite 6-point closed Newton–Cotes quadrature algebraic equation

Uses Software

• KELLEY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An iterative method for large sparse linear systems on a vector computer
• Affine invariant convergence results for Newton's method
• A parallel algorithm for solving block tridiagonal linear systems
• The two-stage arithmetic mean method
• Numerical analysis. A 1st course in scientific computation. Transl. from the German by F. A. Potra and F. Schulz
• Local Convergence of Inexact Newton Methods
• Multi-Splittings of Matrices and Parallel Solution of Linear Systems
• On Steplength Algorithms for a Class of Continuation Methods
• Inexact Newton Methods
• Asymptotic Mesh Independence of Newton–Galerkin Methods via a Refined Mysovskii Theorem
• Affine Invariant Convergence Theorems for Newton’s Method and Extensions to Related Methods
• On Newton-Iterative Methods for the Solution of Systems of Nonlinear Equations
• Numerical Optimization
• Convergence behaviour of inexact Newton methods
• Globally Convergent Inexact Newton Methods
• A Characterization of Superlinear Convergence and Its Application to Quasi-Newton Methods
• Choosing the Forcing Terms in an Inexact Newton Method
• On Best Conditioned Matrices

This page was built for publication: The Newton-arithmetic mean method for the solution of systems of nonlinear equations.