A Matrix Modification Method for Calculating Approximate Solutions to Systems of Linear Equations

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Abstract
An expensive feature of iterative methods for non-linear problems may be the need for frequent solution of systems of linear equations. This paper proposes a method for reducing the amount of such work by approximating the inverse of the coefficient matrix. Unlike previously suggested matrix updating techniques, however, the present method is designed to estimate the discrepancy between the exact and approximate solutions. In this way the accuracy of the approximate solutions can be controlled.