Parallel nonlinear AOR method and its convergence
The paper investigates convergence of parallel nonlinear accelerated overrelaxation (AOR) methods for the solution of large scale systems of nonlinear algebraic equations in the form \(Ax+\varphi(x)=b\), where \(x,b\in \mathbb{R}^n\), \(A\) is a nonsingular matrix and \(\varphi:\mathbb{R}^n\to\mathbb{R}^n\) is a continuous diagonal nonlinear mapping. The AOR method is constructed via a multisplitting of the matrix \(A\). Under the assumptions that \(A\) is an H-matrix and \(\varphi\) satisfies certain monotonicity condition, the global convergence of the above method is proved. For \(A\) being an A-matrix some further result about monotone convergence of the method is established.
parallel nonlinear accelerated overrelaxation methods
large scale systems of nonlinear algebraic equations
scientific article; zbMATH DE number 878519