Author(s)

G.A. Gravvanis

Abstract

Using explicit preconditioned domain decomposition methods for solving singular perturbed linear problems George A. Gravvanis Department of Mathematics, University of the Aegean, Greece Abstract A new class of explicit preconditioned domain decomposition iterative methods in conjunction with approximate inverse arrow matrix techniques is introduced for computing explicitly various families of approximate inverses based on approximate LU-type factorizaton techniques without inverting the decomposition factors. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of linear systems. Applications of the new proposed explicit preconditioned method on SP initial-value problems are discussed and numerical results are given. 1 Introduction Many engineering and scientific problems are described by sparse systems of algebraic equations, which arise when solving Partial Differential Equati

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