Parallel inverse iteration with reorthogonalization
George I. Fann, R.J. Littlefield · University of North Texas Digital Library (University of North Texas) · 1993
A parallel method for finding orthogonal eigenvectors of real symmetric tridiagonal is described. The method uses inverse iteration with repeated Modified Gram-Schmidt (MGS) reorthogonalization of the unconverged iterates for clustered eigenvalues. This approach is more parallelizable than reorthogonalizing against fully converged eigenvectors, as is done by LAPACK's current DSTEIN routine. The new method is found to provide accuracy and speed comparable to DSTEIN's and to have good parallel scalability even for matrices with large clusters of eigenvalues. We present al results for residual and orthogonality tests, plus timings on IBM RS/6000 (sequential) and Intel Touchstone DELTA (parallel) computers.