FINITE DIFFERENCE SCHEMES USING FAST GENERALIZED APPROXIMATE INVERSE BANDED MATRIX TECHNIQUES

摘要

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. Theoretical results on the rate of convergence and estimates of the computational complexity required to reduce the L_∞ - norm of the error by a factor ε are presented. Applications of the method on linear systems are discussed and numerical results are given.