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A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space Dimensions

DOI: 10.4236/am.2016.711108, PP. 1225-1240

Keywords: Adaptive Algorithms, Algorithmic Modelling, Approximate Inverse, Incomplete LU Factorization, Approximate Decomposition, Unsymmetric Linear Systems, Preconditioned Iterative Methods, Systems of Irregular Structure

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Abstract:

A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex computational problems in three space dimensions. The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied. Optimized versions of the proposed approximate inverse are presented using special storage (k-sweep) techniques leading to economical forms of the approximate inverses. Application of the adaptive algorithmic methodologies on a characteristic nonlinear boundary value problem is discussed and numerical results are given.

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