Parallel Computing for the Inverse of SPD matrix

Yan Shen, Yuxing Dai, Zhiliang Zhu
Hunan University, ChangSha, P.R.China
Hunan University, 2017


   title={Parallel Computing for the Inverse of SPD matrix},

   author={Shen, Yan and Dai, Yuxing and Zhu, Zhiliang},



In this paper, we propose a High performance Parallel Computing method for the Inverse of a symmetric positive definite (SPD) matrix. Brought in the reuse of the inverse of diagonal sub blocks technique and Combined with the newest OpenCL parallel computing framework, this methods can improve computing the inverse of SPD matrix effectively. Computing the inverse of SPD matrix can be broken down into three steps: Cholesky decomposition of SPD matrix, computing the inverse of lower triangular matrix, matrix product of triangular matrix and its transpose. Cholesky decomposition in this method can also be modified to correct a matrix which is not positive definite. By making each step parallel, we get a better performance than the current clMAGMA packages about 10x times. Our implementation has cross-platform features and can be used by CPU and GPU without modification.
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