Solution of Nonlinear Problems by a Reduced Rank Modification of the Iteration Matrix

Abstract

An algorithm to compute the solution of nonlinear problems is presented. It makes use of a previously acquired knowledge about a subspace in which the solution is supposed to be mainly contained. This
information is used in order to make a partial modification of the iteration matrix. The modification is made at some steps of the iterative cycle, and it updates the matrix in the directions which are basis of the subspace. The method is here tested by computing the transient nonlinear response in thermal conduction problems.