A lookahead algorithm for the solution of block toeplitz systems

We give a weakly stable algorithm to solve a block Toeplitz system of linear equations. If the lookahead steps taken to compute the parameters of the inversion formula for the block Toeplitz matrix are small compared to the order n of the matrix, the algorithm requires O(n2) floating-point operations. The parameters of the inversion formula are interpreted and computed in a recursive way as solutions of certain interpolation problems given the formal Laurent series based on the data of the block Toeplitz matrix.