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

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https://doi.org/10.1007/978-3-658-16786-8e error of the matrix multiplications appearing in the algorithm. In this paper, we improve the accuracy of the approximate solutions of the Shifted systems generated by the Shifted Block BiCGGR method.
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Von der Arithmetik zur Algebra,when eigenvectors are unnecessary. Our technique is also beneficial in cases where eigenvectors are necessary, because the residual norms of the target eigenpairs can be cheaply computed and monitored during each iteration step of the inner linear solver.
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,“Never Was There More to Do.”,ategorize the recent advances in this field from the perspective of compute-memory tradeoff, which has not been considered in much detail in this area. Benchmark tests reveal that there is a large difference in the memory consumption and performance between the different methods.
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Numerical Integral Eigensolver for a Ring Region on the Complex Plane,avoid a decrease in the computational accuracy of the eigenpairs resulting from locating the quadrature points near the eigenvalues. We implement the proposed method in the SLEPc library, and examine its performance on a supercomputer cluster with many-core architecture.
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Accuracy Improvement of the Shifted Block BiCGGR Method for Linear Systems with Multiple Shifts ande error of the matrix multiplications appearing in the algorithm. In this paper, we improve the accuracy of the approximate solutions of the Shifted systems generated by the Shifted Block BiCGGR method.
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