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A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic
journal contribution
posted on 2016-03-01, 00:00 authored by Gleb BeliakovGleb Beliakov, Y MatiyasevichWe present a parallel algorithm for calculating determinants of matrices in arbitrary precision arithmetic on computer clusters. This algorithm limits data movements between the nodes and computes not only the determinant but also all the minors corresponding to a particular row or column at a little extra cost, and also the determinants and minors of all the leading principal submatrices at no extra cost. We implemented the algorithm in arbitrary precision arithmetic, suitable for very ill conditioned matrices, and empirically estimated the loss of precision. In our scenario the cost of computation is bigger than that of data movement. The algorithm was applied to studies of Riemann’s zeta function.
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Journal
BIT numerical mathematicsVolume
56Issue
1Pagination
33 - 50Publisher
SpringerLocation
Berlin, GermanyPublisher DOI
ISSN
0006-3835eISSN
1572-9125Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2016, SpringerUsage metrics
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