Performance Evaluation of Mixed Precision Algorithms for Solving Sparse Linear Systems

Zounon, Mawussi and Higham, Nicholas J. and Lucas, Craig and Tisseur, Françoise (2020) Performance Evaluation of Mixed Precision Algorithms for Solving Sparse Linear Systems. [MIMS Preprint]

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Abstract

It is well established that mixed precision algorithms that factorize a matrix at a precision lower than the working precision can reduce the execution time of parallel solvers for dense linear systems. Much less is known about the efficiency of mixed precision parallel algorithms for sparse linear systems, and existing work focuses on single core experiments. We evaluate the benefits of using single precision arithmetic in solving a double precision sparse linear systems using multiple cores, focusing on the key components of LU factorization and matrix–vector products. We find that single precision sparse LU factorization is prone to a severe loss of performance due to the intrusion of subnormal numbers. We identify a mechanism that allows cascading fill-ins to generate subnormal numbers and show that automatically flushing subnormals to zero avoids the performance penalties. Our results show that the anticipated speedup of 2 over a double precision LU factorization is obtained only for the very largest of our test problems. For iterative solvers, we find that for the majority of the matrices computing or applying incomplete factorization preconditioners in single precision does not present sufficient performance benefits to justify the loss of accuracy compared with the use of double precision.

Item Type: MIMS Preprint
Uncontrolled Keywords: Mixed precision algorithms, iterative refinement, sparse linear algebra, subnormal numbers
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
MSC 2010, the AMS's Mathematics Subject Classification > 68 Computer science
Divisions: Manchester Institute for the Mathematical Sciences
Depositing User: PhD Mawussi Zounon
Date Deposited: 20 Sep 2020 09:03
Last Modified: 20 Sep 2020 11:39
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2783

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