Search

In this paper we tackle the inversion of large-scale dense matrices via conventional matrix factorizations (LU, Cholesky, LDL T ) and the Gauss-Jordan method on hybrid platforms consisting of a multi-core CPU and a many-core graphics processor (GPU). Specifically, we introduce the different matrix inversion algorithms using a unified framework based on the notation from the FLAME project; we develop hybrid implementations for those matrix operations underlying the algorithms, alternative to those in existing libraries for singleGPU systems; and we perform an extensive experimental study on a platform equipped with state-of-the-art general-purpose architectures from Intel and a “Fermi” GPU from NVIDIA that exposes the efficiency of the different inversion approaches. Our study and experimental results show the simplicity and performance advantage of the GJE-based inversion methods, and the difficulties associated with the symmetric indefinite case.

Summary The solution of linear systems is a recurrent operation in scientific and engineering applications, traditionally addressed via the LU factorization. The Gauss–Huard (GH) algorithm has been introduced as an efficient alternative in modern platforms equipped with accelerators, although this approach presented some functional constraints. In particular, it was not possible to reuse part of the computations in the solution of delayed linear systems or in the inversion of the matrix. Here, we adapt GH to overcome these two deficiencies of GH, yielding new algorithms that exhibit the same computational cost as their corresponding counterparts based on the LU factorization of the matrix. We evaluate the novel GH extensions on the solution of Lyapunov matrix equations via the LRCF-ADI method, validating our approach via experiments with three benchmarks from model order reduction. Copyright © 2017 John Wiley & Sons, Ltd.