You are not logged in.

A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic

Beliakov, Gleb and Matiyasevich, Yuri 2016, A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic, BIT numerical mathematics, vol. 56, no. 1, pp. 33-50, doi: 10.1007/s10543-015-0547-z.

Attached Files
Name Description MIMEType Size Downloads

Title A parallel algorithm for calculation of determinants and minors using arbitrary precision arithmetic
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Matiyasevich, Yuri
Journal name BIT numerical mathematics
Volume number 56
Issue number 1
Start page 33
End page 50
Total pages 18
Publisher Springer
Place of publication Berlin, Germany
Publication date 2016-03
ISSN 0006-3835
Keyword(s) determinant
linear algebra
parallel algorithms
message passing interface
GPU
Riemann’s zeta function
Summary We 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.
Language eng
DOI 10.1007/s10543-015-0547-z
Field of Research 080205 Numerical Computation
0102 Applied Mathematics
0103 Numerical And Computational Mathematics
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2016, Springer
Persistent URL http://hdl.handle.net/10536/DRO/DU:30071079

Document type: Journal Article
Collection: School of Information Technology
Connect to link resolver
 
Unless expressly stated otherwise, the copyright for items in DRO is owned by the author, with all rights reserved.

Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 2 times in TR Web of Science
Scopus Citation Count Cited 1 times in Scopus
Google Scholar Search Google Scholar
Access Statistics: 78 Abstract Views, 3 File Downloads  -  Detailed Statistics
Created: Mon, 07 Mar 2016, 13:50:45 EST

Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.