Titlebook: Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing; EPASA 2015, Tsukuba, Tetsuya Sakurai,Shao-Liang Zhang,Ta

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978-3-319-87309-1Springer International Publishing AG 2017

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Computation of Eigenvectors for a Specially Structured Banded Matrix,eigenvectors. We show that the eigenvector entries are arranged radiating out from the origin on the complex plane. This property enables us to efficiently compute all the eigenvectors. Although the intended matrix has complex eigenvalues, the proposed method can compute all the complex eigenvectors using only arithmetic of real numbers.

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Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing978-3-319-62426-6Series ISSN 1439-7358 Series E-ISSN 2197-7100

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. In this paper, we provide an error resilience strategy of a Rayleigh–Ritz type complex moment-based parallel eigensolver for solving generalized eigenvalue problems. Our strategy is based on an error bound of the eigensolver in the case that soft-errors like bit-flip occur. Using the error bound,

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Geowissenschaftsdidaktische Forschung,cution time in parallel processing owing to the communication cost and the number of floating-point operations. To overcome this problem, we focus on real symmetric band eigensolvers proposed by Gupta and Murata since their eigensolvers are composed of the bisection and inverse iteration algorithms