GPU acceleration of splitting schemes applied to differential matrix\n equations

2018/05/23 by Hermann Mena, Mena, Hermann, Lena-Maria Pfurtscheller +3
Computer Science · Mathematics · Engineering · #Matrix Theory and Algorithms #Numerical methods for differential equations #Advanced Numerical Methods in Computational Mathematics

paper · pdf · doi:10.48550/arxiv.1805.08990

Abstract

We consider differential Lyapunov and Riccati equations, and generalized\nversions thereof. Such equations arise in many different areas and are\nespecially important within the field of optimal control. In order to\napproximate their solution, one may use several different kinds of numerical\nmethods. Of these, splitting schemes are often a very competitive choice. In\nthis article, we investigate the use of graphical processing units (GPUs) to\nparallelize such schemes and thereby further increase their effectiveness.\nAccording to our numerical experiments, large speed-ups are often observed for\nsufficiently large matrices. We also provide a comparison between different\nsplitting strategies, demonstrating that splitting the equations into a\nmoderate number of subproblems is generally optimal.\n

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