Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53902#.VNsFVSzQrzE Author(s) Mohammad M. Tabanjeh * Affiliation(s) Department of Mathematics and Computer Science, Virginia State University, Petersburg, VA, USA . ABSTRACT Newton’s iteration is a fundamental tool for numerical solutions of systems of equations. The well-known iteration rapidly refines a crude initial approximation X 0 to the inverse of a general nonsingular matrix. In this paper, we will extend and apply this method to n × n structured matrices M , in which matrix multiplication has a lower computational cost. These matrices can be represented by their short generators which allow faster computations based on the displacement operators tool. However, the length of the generators is tend to grow and the iterations do not preserve matrix structure. So, the main goal is to control the growth of the len...
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