DOUBLE POWER METHOD ITERATION FOR PARALLEL EIGENVALUE PROBLEM

K Rhofir,A Radid,M Ameur

doi:10.12732/ijpam.v108i4.19

Abstract

In this paper, we introduce the double power iteration method witch can be seen as an extension of the classical power iteration in the sense that we calculate the two dominants eigenvalues at each stage. This work aims to propose a solution of slow convergence problem to the power iteration method and the calculation of the second dominant eigenvalue. We develop a parallel iterative procedure for the calculation of eigenvalues of a given matrix and we can expressed this method as a Quadrant Interlocking Factorization (QIF) which introduced by (7) and studied by (8)-(9) in other works.

Highlights

The power iteration method approximates only one eigenvalue of a matrix, it remains useful for certain computational problems
We obtain a sequence of matrices A(1), A(2), . . . which in general reduces to an upper triangular matrix
We present a double power iteration as iterative procedure to calculate the two dominants eigenvalues at each stage

Summary

Introduction

The power iteration method approximates only one eigenvalue of a matrix, it remains useful for certain computational problems. Rutishauser [5] proposed the LR algorithm for the calculation of the eigenvalues of a A In this procedure, we obtain a sequence of matrices A(1), A(2), . We present a double power iteration as iterative procedure to calculate the two dominants eigenvalues at each stage. This procedure still a variants of LR algorithm and the eigenvalues are obtained from simple 2 × 2 matrices derived from the main and cross diagonals of the limit matrix. We start by giving mathematical framework for double power iteration algorithm for computing the two dominant eigenelements of a matrix A. We factorize A in the form like those in [7] to evaluate all eigenvalues and we give an easy way to the solution of linear equation

Double Power Iteration Method

Matrix Factorization