Division algorithms for continued fractions and the Padé table

@article{Bultheel1980DivisionAF,
  title={Division algorithms for continued fractions and the Pad{\'e} table},
  author={Adhemar Bultheel},
  journal={Journal of Computational and Applied Mathematics},
  year={1980},
  volume={6},
  pages={259-266}
}
  • A. Bultheel
  • Published 1 December 1980
  • Mathematics
  • Journal of Computational and Applied Mathematics
Recursive algorithms for the Padé table : Two approaches
TLDR
The factorization interpretation links together the continued fraction approach and the recursive Pade computation in a natural way.
Recursive algorithms for the matrix Padé problem
Abstract. A matrix triangularization interpretation is given for the recursive algorithms computing the Padd approximants along a certain path in the Padd table, which makes it possible to unify all
Pade Approximation in One and More Variables
We first recall results from univariate Pade approximation theory (UPA). The recursive ∈-algorithm and the continued fraction representation obtained from the qd algorithm are given for the normal
Recursive algorithms for nonnormal Padé-tables
TLDR
The Berlekamp-Massey algorithm computes among other polynomials the denominators of the elements of the Pade table that are on the descending diagonal as far as they exist and this algorithm works for nonnormal Pade tables too.
Applications of Pade approximants and continued fractions in systems theory
TLDR
Some known applications of Pade approximants and continued fractions in the theory of linear systems, digital filtering and network theory are summarized.
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References

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Recursive algorithms for the Padé table : Two approaches
TLDR
The factorization interpretation links together the continued fraction approach and the recursive Pade computation in a natural way.
The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis
  • W. Gragg
  • Mathematics, Computer Science
  • 1972
TLDR
Normality criteria for the Pade table, which provide existence theorems for the algorithms, are developed and possible extensions to Laurent series are indicated.
The Laurent-Pade Table
TLDR
Basic existence, uniqueness and algorithmic results are established for the Laurent-Pade table and numerical experience with 'near best' uniform rational approximation to (e sup x) on (-1, 1) is related.
Symbolic Computation of Padé Approximants
  • K. Geddes
  • Mathematics, Computer Science
    TOMS
  • 1979
TLDR
A symbolic manipulation algorithm is developed to compute Pad~ approximants for power series with polynomial coefficients based on a new fraction-free ehmmation algorithm for symmetric mdefimte systems of linear equatmns.
A Property of Euclid’s Algorithm and an Application to Padé Approximation
If a and b are fixed polynomials with $\deg ( a ) > \deg ( b )$, we show that all solutions to the congruence $qb \equiv p( {\bmod a} )$ with $\deg ( q ) + \deg ( p ) < \deg ( a )$ can be obtained
Recursive algorithms for nonnormal Padé-tables
TLDR
The Berlekamp-Massey algorithm computes among other polynomials the denominators of the elements of the Pade table that are on the descending diagonal as far as they exist and this algorithm works for nonnormal Pade tables too.
A class of algorithms for obtaining rational approximants to functions which are defined by power series
The problem of converting power series to different types of continued fractions is treated by demonstrating the generality of application of an often neglected class of algorithms. As an example, a
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