# 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} }

## 24 Citations

Recursive algorithms for the Padé table : Two approaches

- Mathematics, Computer Science
- 1979

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

- Computer Science
- 1980

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

- Mathematics
- 1992

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…

On the use of a corresponding sequence algorithm for d-fractions

- Computer Science, Mathematics
- 1991

Recursive algorithms for nonnormal Padé-tables

- Computer Science
- 1980

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

- Mathematics
- 1984

Some known applications of Pade approximants and continued fractions in the theory of linear systems, digital filtering and network theory are summarized.

## References

SHOWING 1-10 OF 29 REFERENCES

Recursive algorithms for the Padé table : Two approaches

- Mathematics, Computer Science
- 1979

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

- Mathematics, Computer Science
- 1972

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

- MathematicsIFIP Congress
- 1974

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.

A new look at the Padé table and the different methods for computing its elements

- Computer Science, Mathematics
- 1975

Symbolic Computation of Padé Approximants

- Mathematics, Computer ScienceTOMS
- 1979

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

- Mathematics
- 1978

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

- Computer Science
- 1980

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

- Mathematics
- 1977

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…