A GPU‐aware mixed‐precision solver for low‐rank algebraic Riccati equations. (28th February 2018)

• Record Type: Journal Article
• Authors: Benner, Peter; Dufrechou, Ernesto; Ezzatti, Pablo; Remón, Alfredo; Saak, Jens
• Other Names: Ezzatti Pablo guestEditor.; Quintana‐Ortí Enrique S. guestEditor.; Remón Alfredo guestEditor.; Saak Jens guestEditor.
• Is Part Of: Concurrency and computation. Volume 31:Number 6(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-02-28
• Subjects: algebraic Riccati equations -- graphics processing units -- low‐rank -- matrix equations -- mixed precision; Parallel processing (Electronic computers) -- Periodicals; Parallel computers -- Periodicals; 004.35
• DOI: 10.1002/cpe.4462
• Languages: English
• ISSNs: 1532-0626

Abstract

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.