The efficient and reliable subspace iteration algorithm using the block algorithm is proposed. The block algorithm is the method dividing the eigenpairs into the various blocks when a large number of eigenpairs are required.
One of the key for the convergence is the carefully selected initial vector. As the initial vector, the proposed method uses the modified Ritz vector not for missing the required eigenpairs and the quasi-static Ritz vector in order to represent the eigenvectors corresponding to the high frequencies efficiently. Applying the quasi-static Ritz vector, it always requires the shift so that the proper shift using the geometric average is proposed.
To maximize efficiency, this paper estimates the proper number of block based on the theoretical amount of calculation in the subspace iteration. And it also considers the problems generated in a process of combining various algorithms and the solutions to the problems.
Various numerical results show that the proposed subspace iteration algorithm is very efficient, reliable ,and accurate.
