Matrix inversion on CPU-GPU platforms with applications in control theory

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.