Homitopy Method For Solving Matrlk Elgenvalue

This article studies the homotopy algorithm using matrix eigenvalue problem. Eigenvalue problem in mathematics and other fields, there are many applications, such as the stability of linear differential equations and asymptotic estimation of the sphere stability point of solving quadratic eigenvalue problems and constraints. Homotopy method is developed seventies began to solve nonlinear problems is an effective way. It is to overcome the initial difficulties of the traditional iterative method selected, and the weakness of local convergence, homotopy algorithm, the selection of the initial value is not strictly limited to ensure global convergence, and very easy to implement parallel computing.This article mainly: First, set the eigenvalue problem related to algorithm development history of its development, research, and the history of the development of homotopy algorithm, etc.Secondly, the study of three diagonal matrices, some theoretical analysis and through the corresponding formula tridiagonal matrix eigenvalues and eigenvectors, which will help with the homotopy algorithm to solve the eigenvalue comparison.Finally, focusing on the development of the homotopy algorithm and the basic idea, explained the basic theory of the homotopy algorithm is given Symmetric Matrix Eigenvalue homotopic mapping and related properties of the structure, the homotopy path tracking solution, and According to the error analysis of specific examples. And the homotopy method and the comparative analysis of other schemes.