The Newton-arithmetic mean method for the solution of systems of nonlinear equations.
Newton-iterative methods for large systems of nonlinear equations with a block-structured Jacobian are considered. For solving the linear system at each stage of Newton's method the arithmetic mean method is considered, which is based on two particular block-diagonal splitting matrices for the Jacobian, and, therefore, is well suited for implementation on parallel computers. The convergence of the method is analyzed for systems whose Jacobian satisfies an affine invariant Lipschitz condition. The case of weakly nonlinear systems, which arise, for example, from the discretization of semi-linear elliptic systems, is considered in more details, and numerical experiments are reported for such a problem.
scientific article; zbMATH DE number 1861282
scientific article