Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations

In a recent paper, we introduced a new look-ahead algorithm for recursively computing Padé approximants. This algorithm generates a subsequence of the Padé approximants on two adjacent rows (defined by fixed numerator degree) of the Padé table. Its two basic versions reduce to the classical Levinson and Schur algorithms if no look-ahead is required. In this paper, we show that the computational overhead of the look-ahead steps in the O(N2) versions of the look-ahead Levinson- and the look-ahead Schur-type algorithm can be further reduced. algorithms are used to solve Toeplitz systems of equations Tx = b, then the corresponding block LDU decompositions of T−1 or T, respectively, can be found with less computational effort than with any other look-ahead algorithm available today.