An asynchronous parallel algorithm for solving a class of nonlinear simultaneous equations
The system of nonlinear algebraic equations \(Ax+\phi (x)=0,\) where A is an \(n\times n\) M-matrix and \(\phi\) is a diagonal isotone continuous mapping, is treated with parallel asynchronous algorithms, namely, Schwarz-alternating procedure inspired versions of Jacobi and relaxation schemes. Convergence rates are shown to be at least linear. Further, some numerical results are exhibited that were obtained through application of the developed method to a nonlinear elliptic equation discretized with finite differences, which thus amounts to a domain decomposition technique.
scientific article; zbMATH DE number 4205878