Abstract
The Lanczos algorithm is among the most frequently used techniques for computing a few dominant eigenvalues of a large sparse non-symmetric matrix. When variants of this algorithm are implemented on distributed-memory computers, the synchronization time spent in computing dot products is increasingly limiting the parallel scalability. The goal of s-step algorithms is to reduce the harmful influence of dot products on the parallel performance by grouping several of these operations for joint execution; thus, plummeting synchronization time when using a large number of processes. This paper extends the non-symmetric s-step Lanczos method introduced by Kim and Chronopoulos (J. Comput. Appl. Math., 42(3), 357–374, 1992) by a novel normalization scheme. Compared to the unnormalized algorithm, the normalized variant improves numerical stability and reduces the possibility of breakdowns.
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Feuerriegel, S., Bücker, H.M. (2013). A Normalization Scheme for the Non-symmetric s-Step Lanczos Algorithm. In: Aversa, R., Kołodziej, J., Zhang, J., Amato, F., Fortino, G. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2013. Lecture Notes in Computer Science, vol 8286. Springer, Cham. https://doi.org/10.1007/978-3-319-03889-6_4
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DOI: https://doi.org/10.1007/978-3-319-03889-6_4
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