Tensor-Krylov Methods for Large Sparse Systems of Nonlinear Equations

In this paper, we describe tensor methods for large sparse systems of nonlinear equations based on Krylov subspace techniques for approximately solving the linear systems that are required in each tensor iteration. We refer to a method in this class as a tensor-Krylov algorithm. We describe comparative testing for a tensor-Krylov implementation versus an analogous implementation based on a Newton-Krylov method. The test results show that tensor-Krylov methods are more efficient and robust than Newton-Krylov methods. Key words. tensor methods, nonlinear equations, sparse problems, large scale optimization, Krylov methods, GMRES Centre Europ'een de Recherche et de Formation Avanc'ee en Calcul Scientifique (CERFACS), 42 Avenue Gustave Coriolis, 31057 Toulouse Cedex, France, Ali.Bouaricha@cerfacs.fr. Contents 1 Introduction 3 2 Overview of Tensor Methods for Large Sparse Nonlinear Equations 3 3 Krylov Subspace Methods 6 3.1 GMRES Method : : : : : : : : : : : : : : : : : : : : : : : ..