A fast parallel Gauss Jordan algorithm for matrix inversion using CUDA

• Current literature suggests time complexity of matrix inversion is 2 or higher.
• This paper redesigns the Gauss Jordan algorithm for matrix inversion on CUDA platform.
• The algorithm exploits large scale parallelization of a massively multithreaded GPU.
• Performance metrics of the algorithm are compared with CPU based parallel methods.
• Time complexity of our method scales as n as long as n2 threads are supported by GPU.

The ability to invert large matrices quickly and accurately determines the effectiveness of a computational tool. Current literature suggests that time complexity of matrix inversion is 2 or higher. This paper redesigns the Gauss Jordan algorithm for matrix inversion on a CUDA platform to exploit the large scale parallelization feature of a massively multithreaded GPU. The algorithm is tested for various types of matrices and the performance metrics are studied and compared with CPU based parallel methods. We show that the time complexity of matrix inversion scales as n as long as n2 threads can be supported by the GPU.