A method for updating Cholesky factorization of a band matrix

Abstract

A method is presented for updating the Cholesky factorization of a band symmetric matrix modified by a rank-one matrix which has the same band width. Problems which could involve applications of such a method arise frequently in plasticity and structural optimization where repeated solutions of a band algebraic system with a changing matrix are needed. The Cholesky factorization of a stiffness matrix can be updated after modifying a local stiffness matrix which can be written as a sum of a few rank-one matrices. The number of operations required for the updating is of the order mn or less, where n is the dimension of the global matrix and m is its half band width (including the diagonal).