Fasi, Massimiliano and Higham, Nicholas J. (2020) Generating extremescale matrices with specified singular values or condition numbers. [MIMS Preprint] (Unpublished)
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Abstract
A widely used form of test matrix is the randsvd matrix constructed as the product A = USV*, where U and V are random orthogonal or unitary matrices from the Haar distribution and S is a diagonal matrix of singular values. Such matrices are random but have a specified singular value distribution. The cost of forming an mbyn randsvd matrix is m³ + n³ flops, which is prohibitively expensive at extreme scale; moreover, the randsvd construction requires a significant amount of communication, making it unsuitable for distributed memory environments. By dropping the requirement that U and V be Haar distributed and that both be random, we derive new algorithms for forming A that have cost linear in the number of matrix elements and require a low amount of communication and synchronization. We specialize these algorithms to generating matrices with specified 2norm condition number. Numerical experiments show that the algorithms have excellent efficiency and scalability.
Item Type:  MIMS Preprint 

Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis 
Depositing User:  Mr Massimiliano Fasi 
Date Deposited:  20 Oct 2020 10:59 
Last Modified:  20 Oct 2020 10:59 
URI:  http://eprints.maths.manchester.ac.uk/id/eprint/2786 
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Generating extremescale matrices with specified singular values or condition numbers. (deposited 27 Mar 2020 19:10)
 Generating extremescale matrices with specified singular values or condition numbers. (deposited 20 Oct 2020 10:59) [Currently Displayed]
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