Generalized Purcell method and its applications

Sayed Masuleh | Morteza Rahmani

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=59
Date :  2008/12/31
Publish in :    International Journal of Applied Mathematics


Keywords :Generalized, Purcell

Abstract :

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In this paper, the theoretical and numerical aspects of the generalized Purcell method for solving a system of homogeneous linear equations are provided. The novel row and the column pivoting are defined, that help to prove the stability of the method. The proposed method is generalized for solving eigenvalue and eigenvector problems. The advantages of the method are: 1. The presented method generates the set of linearly dependent rows of a matrix, say A, and its multiple independent solutions in solving Ax = 0; 2. It gives the eigenvectors of a matrix A if there exists an eigenvalue with geometric multiplicity; 3. For a real and symmetric matrix it will gives an a posteriori error estimation; and 4. Also is proved that the complexity of the method is approximately half of the complexity of the Gaussian elimination method. Finally, in order to indicate the reliability and efficiency of the method, comparisons with the power method are made.