Abstract
We present general recurrences for the Padé table that allow us to skip ill- conditioned Padé approximants while we proceed along a row of the table. In conjunction with a certain inversion formula for Toeplitz matrices, these recurrences form the basis for fast algorithms for solving non-Hermitian Toeplitz systems. Under the assumption that the lookahead step size (i.e., the number of successive skipped approximants) remains bounded, we give both O( N 2) and O( N log 2 N) algorithms which are (presumably) weakly stable. With little additional work, still in O( N 2) operations, we can also obtain a decomposition of the Toeplitz matrix T according to TR = LD, where R is upper triangular, L is unit lower triangular, and D is block-diagonal. The relation to continued fractions is also discussed.
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