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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 GramSchmidt orthogonalization is used, and this causes a bottleneck in parallel computing. In this paper, the use of the compact WY… (More)

- Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
- ArXiv
- 2012

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)

In this paper, we compare with the inverse iteration algorithms on PowerXCell 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 algorithms… (More)

- Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
- 2014 22nd Euromicro International Conference on…
- 2014

Effective GPU implementations of an inverse iteration algorithm with reorthogonalization are proposed for computing eigenvectors of symmetric tridiagonal matrices. The key to effectively accelerating the inverse iteration algorithm in GPU computing is the adoption of reorthogonalization code optimal for the GPU. The CGS2 algorithm and the compact WY… (More)

The continued fraction method for isolating the positive roots of a univariate polynomial equation is based on Vincent’s theorem, which computes all of the real roots of polynomial equations. In this paper, we propose two new lower bounds which accelerate the fraction method. The two proposed bounds are derived from a theorem stated by Akritas et al., and… (More)

- Hiroyuki Ishigami, Kinji Kimura, Yoshimasa Nakamura
- 2015 10th International Conference on P2P…
- 2015

In order to accelerate the subset computation of eigenpairs for real symmetric tridiagonal matrices on shared-memory multi-core processors, a parallel symmetric tridiagonal eigensolver is proposed, which computes eigenvalues of target matrices using the parallel bisection algorithm and computes the corresponding eigenvectors using the block inverse… (More)

The Golub-Kahan-Lanczos algorithm with reorthogonalization (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)

- H Ishigami
- Kangogaku zasshi
- 1988

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