On the Solution of Boundary Value Problems by Using Fast Generalized Approximate Inverse Banded Matrix Techniques

A class of finite difference schemes in conjunction with approximate inverse banded matrix techniques based on the concept of LU-type factorization procedures is introduced for computing fast explicit approximate inverses. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of banded linear systems. A theorem on the rate of convergence and estimates of the computational complexity required to reduce the L-norm of the error is presented. Applications of the method on linear and non-linear systems are discussed and numerical results are given.