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— A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tridiagonal matrix on parallel computers is developed. In the classical inverse iteration algorithm, the modified Gram-Schmidt orthogonalization is used, and this causes a bottleneck in parallel computing. In this paper, the use of the compact WY… (More)

A new inverse iteration algorithm that can be used to compute all the eigenvectors of a real symmetric tri-diagonal matrix on parallel computers is developed. The modified Gram-Schmidt orthogonalization is used in the classical inverse iteration. This algorithm is sequential and causes a bottleneck in parallel computing. In this paper, the use of the… (More)

— The Golub-Kahan-Lanczos algorithm with re-orthogonalization (GKLR algorithm) is an algorithm for computing a subset of singular triplets for large-scale sparse matrices. The reorthogonalization tends to become a bottleneck of elapsed time, as the iteration number of the GKLR algorithm increases. In this paper, OpenMP-based parallel implementation of the… (More)

— In this paper, we compare with the inverse iteration algorithms on PowerXCell T M 8i processor, which has been known as a heterogeneous environment. When some of all the eigenvalues are close together or there are clusters of eigenvalues, reorthogonalization must be adopted to all the eigenvectors associated with such eigenvalues. Reorthogonalization… (More)

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