Parallelization of Toeplitz Solvers

We shall describe parallel algorithms for solving Toeplitz and block Toeplitz systems, based on the Levinson type methods implemented in serial in the Toeplitz Package (by Arushanian et al. [1]). A matrix A, with blocks A i , j , has block Toeplitz structure if the blocks satisfy A i , j = A j − i for all i, j such that 0 ≤ i, j ≤ n − 1 and each block is a general matrix. The implementation and performance of these algorithms on MIMD shared memory machines will be discussed. It will be shown that the contribution of the inner product calculations to the time complexity is negligible for typical applications.

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