A SEQUENTIAL SUBSPACE PROJECTION METHOD FOR LINEAR SYMMETRIC EIGENVALUE PROBLEM

In this paper, we introduce a geometric model for linear symmetric eigenvalue problem, which is motivated by the fact that any eigenvalue of a symmetric positive definite matrix A is the reciprocal of the square length of an axis of the ellipsoid xTAx = 1. Hence, to find the largest eigenvalue is equivalent to calculate the shortest axis of the corresponding ellipsoid. Two sequential subspace projection algorithms based on this idea are proposed, and we establish the global convergence and local linear convergence rate of our proposed algorithms. Numerical experiments demonstrate that our algorithm outperforms the MATLAB built-in solver "EIGS" which calls the famous package "ARPACK".