Preprint No. MPIMD/12-02

Title: Matrix Inversion on CPU-GPU Platforms with Applications in Control Theory

Author(s): Peter Benner, Pablo Ezzatti, Enrique S. Quintana-Ortí, Alfredo Remón


Date: 2012-02-01


In this paper we tackle the inversion of large-scale dense matrices via conventional matrix factorizations (LU, Cholesky, LDLT ) 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 single-GPU 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.


author = {Peter Benner and Pablo Ezzatti and Enrique S. Quintana-Ortí and Alfredo Remón},
title = {Matrix Inversion on CPU-GPU Platforms with Applications in Control Theory},
number = {MPIMD/12-02},
month = feb,
year = 2012,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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