Split-step algorithm for matrix preconditioning and inversion on systolic arrays
P. Paparao, A. Ghosh · IEE Proceedings E Computers and Digital Techniques · 1989
New algorithms for preconditioning and inversion of symmetric positive-definite matrices are proposed in this paper. These algorithms have a parallel structure and are suitable for realisation on systolic arrays. The algorithms are based on the repeated use of a polynomial preconditioning technique. Matrix-matrix multiplications constitute the major computations in these algorithms. On a systolic array, the total time for either preconditioning or inversion of an (N × N) matrix is of the order of N. The implementational details of the algorithm on systolic arrays are outlined. Preliminary theoretical analysis on the convergence rate of the algorithms for a specific input parameter combination is presented along with the results of numerical experiments on several matrices.