Multivariate Padé Approximation and Its Application in Solving Systems of Nonlinear Equations

Abstract

For a certain kind of multivariate Padé approximation problems, we establish in this paper some results about the solvability and uniqueness of its solution. We also give the necessary and sufficient conditions for the continuity of Padé approximation operator. The application of such approximations in finding solutions of systems of nonlinear equations is considered, and some numerical examples are given, in which it is shown that the Padé methods are more effective than the Newton methods in some cases.