A method is shown that transforms the problem of inverting an ill-conditioned matrix to one of inverting a diagonally dominant matrix. An error analysis is outlined and the method is compared in theory and in result with the commonly used iterative methods. This direct method is demonstrated to be the limiting case of an nth-order iterative procedure as n approaches infinity. Examples are given that show the advantages of the direct method even under adverse conditions. The unreliability of the convergence of the iterative technique due to computational errors is also discussed.
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