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

[摘要] In a recent paper, we introduced a new look-ahead algorithm for recursively computing Pade approximants. This algorithm generates a subsequence of the Pade approximants on two adjacent rows (defined by fixed numerator degree) of the Pade 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(N-2) versions of the look-ahead Levinson-and the look-ahead Schur-type algorithm can be further reduced. If the 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.

[发布日期] 1997-11-28

[关键词] Pade approximation;row recurrence;fast algorithm;sawtooth recurrence;look-ahead;toeplitz matrix;Levinson algorithm;Schur algorithm;biorthogonal polynomials