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A GPU‐aware mixed‐precision solver for low‐rank algebraic Riccati equations
Author(s) -
Benner Peter,
Dufrechou Ernesto,
Ezzatti Pablo,
Remón Alfredo,
Saak Jens
Publication year - 2018
Publication title -
concurrency and computation: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.309
H-Index - 67
eISSN - 1532-0634
pISSN - 1532-0626
DOI - 10.1002/cpe.4462
Subject(s) - solver , computer science , iterative refinement , rank (graph theory) , algebraic riccati equation , single precision floating point format , double precision floating point format , arbitrary precision arithmetic , sign (mathematics) , algorithm , algebraic number , parallel computing , riccati equation , mathematical optimization , mathematics , floating point , differential equation , mathematical analysis , combinatorics , programming language
Summary We investigate different alternatives for the solution of algebraic Riccati equations on hybrid hardware platforms (ie, CPUs+GPUs). We evaluate a mixed‐precision approach that uses single‐precision arithmetic to obtain an approximation to the solution and later improve it to the desired precision, applying some steps of an economic iterative refinement. This method exploits the higher performance of the hardware to accelerate the solver when single‐precision arithmetic is employed and simultaneously obtains a high‐accuracy solution with the iterative refinement. We extend this approach to exploit the low‐rank property of the equation, when possible, to further improve its efficiency. The experimental evaluation shows that the mixed‐precision approach reports time and energy savings and provides similar or even more accurate solutions than well‐known methods like the sign function iteration or the structure‐preserving doubling algorithm.