Research Of Parallel Circular Algorithm For Solving Matrices Eigenvalue

In this paper, the parallel algorithm for finding; matrices eigenvalue and its internal mechanism are thoroughly researched by situation of research at home and abroad. The matrices eigenvalue problem come down to the problem for solving roots of a polynomial, thereafter it is solved by circular arithmetic.Firstly, based on the parallel Halley circular iteration method, the asynchronous parallel algorithm and fast parallel Halley algorithm for finding all zeros of a polynomial are constructed. The convergence rate of third order and seventh order is obtained under the similar condition of Halley iteration method, by which the calculation efficiency of Halley iteration method is improved greatly.Secondly, the method for finding initial circular of symmetric matrices is presented on the based of the dichotomy. The method for finding initial circular of nonsymmetric matrices is obtained by utilizing the distribution theory of matrices eigenvalue, which satisfies the initial condition of circular iteration.Finally, these methods are applied to solve eigenvalues of symmetric matrices and nonsymmetric matrices, by which the asynchronous parallel circular algorithm and fast parallel Halley circular algorithm are obtained for solving all eigenvalues of matrices.The algorithm is proved to be faster than the dichotomy which is based on the distribution theory of matrices eigenvalues by theoretical analysis and numerical results. It is reasonable on theory and effective on computational practice.