Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations
✍ Scribed by Marlis Hochbruck
- Book ID
- 104338504
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 982 KB
- Volume
- 86
- Category
- Article
- ISSN
- 0377-0427
No coin nor oath required. For personal study only.
✦ Synopsis
In a recent paper, we introduced a new look-ahead algorithm for recursively computing Pad6 approximants. This algorithm generates a subsequence of the Pad6 approximants on two adjacent rows (defined by fixed numerator degree) of the Pad6 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.