A new vector field method for eigen-decomposition of symmetric matrices

We study a new approach to eigen-decomposition of symmetric matrices, called the vector field method. In contrast to the methods currently in use, the vector field method computes an eigenvector by computing a discrete approximation to the integral curve of a special tangent vector field on the unit sphere. The optimization problems embedded in each iteration of the vector field algorithms admit closed-form solutions making the vector field approach promisingly efficient.