Abstract
In the improved scheme advanced in this paper, a series of initial vectors are used for one-by-one iteration successively. The method combines the strong points of both the subspace iteration method and the Ritz vector method. Compared with the Ritz vector method, the scheme retains the use of a single vector for inverse iteration, so the computing time may remain similar to that of the Ritz method, but much less than that of the subspace iteration method. Yet the scheme may be compared with the latter in accuracy, since theoretically the convergence for multiple eigenvalue is proved. In the same number of iterations, the accuracy of the scheme is superior to that of the Ritz vector method and the Lanczos method.
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