Stable row recurrences for the Padé table and generically superfast lookahead solvers for non-Hermitian Toeplitz systems

@inproceedings{Gutknecht1993StableRR,
  title={Stable row recurrences for the Pad{\'e} table and generically superfast lookahead solvers for non-Hermitian Toeplitz systems},
  author={Martin H. Gutknecht},
  year={1993}
}
Abstract We present general recurrences for the Pade table that allow us to skip ill- conditioned Pade 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… CONTINUE READING
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