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Direct Technique for Improving a Matrix Inverse

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1 Author(s)
Sitton, G.A. ; IBM Scientific Center, 6900 Fannin Street, Houston, Texas 77001, USA

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.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:15 ,  Issue: 5 )