ACCELERATED REDUCTION OF SUBSPACE UPPER BOUND BY MULTIPLE INVERSE ITERATION

The subspace iteration method is a popular and efficient approximate eigensolution technique for systems with a large number of degrees of freedom. This paper investigates the underlying physical concepts and mathematical background of the subspace iteration technique, and provides an explanation for the slow convergence rate of the higher required eigenpairs. A new acceleration approach, based on an estimate of each eigenvalue's ultimate rate of convergence, is developed and discussed. The method is implemented and tested on two sample numerical analyses, and compared to previous research by the authors. Research into combining this acceleration approach with other acceleration techniques is currently being performed, and shows much promise for producing a very efficient eigenproblem solving technique.