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From Euclid to Padé
Contents
1 Introduction
1.1 Exemplifying the Chinese remainder theorem
1.2 Exemplifying the decomposition of rational functions
1.3 Organization of this paper
2 Algorithms to compute the Bezout's coefficients
2.1 Euclidean versus principal
2.2 Euclidean algorithm, then back
2.3 Straightforward Bezout's algorithm
2.4 Matricial writing
2.5 Centered algorithm
3 Polynomials
4 Continued fractions
4.1 Confrac expansion of a rational
4.2 Some theorems about centered convergents
4.3 Periodic expansion of
4.4 Interval arithmetic and rationality checking
5 Padé approximants
5.1 Obtaining Padé approximants
5.2 Quotients in arithmetical progression
6 Accelerations
6.1 Describing some experiments
6.2 Almost but not everywhere
6.3 Divide and conquer
7 Concluding remarks
Bibliography
Bibliography
Contents
Previous:
Bibliography
Up:
From Euclid to Padé
douillet@ensait.fr
2005-02-09