Do Iterative Solvers Benefit from Approximate Computing? An Evaluation Study Considering Orthogonal Approximation Methods

Abstract

Employing algorithms of scientific computing often comes in hand with finding a trade-off between accuracy and performance. Novel parallel hardware and algorithms only slightly improve these issues due to the increasing size of the problems. While high accuracy is inevitable for most problems, there are parts in scientific computing that allow us to introduce approximation. Therefore, in this paper we give answers to the following questions: (1) Can we exploit different approximate computing strategies in scientific computing? (2) Is there a strategy to combine approaches? To answer these questions, we apply different approximation strategies to a widely used iterative solver for linear systems of equations. We show the advantages and the limits of each strategy and a way to configure a combination of strategies according to a given relative error. Combining orthogonal strategies as an overall concept gives us significant opportunities to increase the performance.