Further optimized look-ahead recurrences for adjacent rows in the Padé table and Toeplitz matrix factorizations
The look-ahead algorithm of \textit{M. H. Gutknecht} and \textit{M. Hochbruck} [BIT 36, No. 2, 264-286 (1996; Zbl 0852.65025)] for computing the \((0,N)\) Padé form of a formal Laurent series with complex coefficients is improved. Two versions (Levinson-type and Schur-type) of the algorithm are considered. When the algorithms are used to solve Toeplitz systems of linear equations then the block LDU decompositions of the system matrix and its inverse can be found with less computational effort compared with other existing look-ahead algorithms. The main features of the algorithm are that it performs look-ahead steps of minimum size and that it reduces to the classical Levinson or Schur algorithm if only regular steps of size 1 are performed.
scientific article; zbMATH DE number 1115934