Gauss-Jordan reduction: a brief history
American Mathematical Monthly
A Strassen-Newton algorithm for high-speed parallelizable matrix inversion
Proceedings of the 1988 ACM/IEEE conference on Supercomputing
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Efficient algorithms for computing a strong rank-revealing QR factorization
SIAM Journal on Scientific Computing
Applied numerical linear algebra
Applied numerical linear algebra
Group-theoretic Algorithms for Matrix Multiplication
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An Operator Factorization Method for Restoration of Blurred Images
IEEE Transactions on Computers
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
GPU in Haptic Rendering of Deformable Objects
EuroHaptics '08 Proceedings of the 6th international conference on Haptics: Perception, Devices and Scenarios
On the GPGPU parallelization issues of finite element approximate inverse preconditioning
Journal of Computational and Applied Mathematics
CUDA Application Design and Development
CUDA Application Design and Development
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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 n^2 threads can be supported by the GPU.