A Jacobi-based parallel algorithm for matrix inverse computations

In this paper we propose a faster variation of one-sided Jacobi algorithm. We bring the idea of Fast-Givens rotation and utilize it in Jacobi algorithm to generate a so-called Fast-onesided Jacobi algorithm, which can be utilized to calculate matrix inverse in parallel environment in a faster speed without losing any precision. Then, we give a simpler and faster variation of the new algorithm. We use Taylor expansion to approximate the parameter to avoid calculation of square roots. Numerical results are presented to validate the theoretical analysis.