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Nested multivariate Padé approximants

✍ Scribed by Philippe Guillaume

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
578 KB
Volume
82
Category
Article
ISSN
0377-0427

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✦ Synopsis

A new class of multivariate Pad6 approximants is introduced. When dealing with two variables x and y, the approach consists in applying the Pad6 approximation with respect to y to the coefficients of the Pad6 approximation with respect to x. This technique has a natural extension to n variables, and is well adapted to programming in any usual language. The advantage of the method is that the algorithm uses only univariate Pad6 approximation. As a consequence, only small systems need to be solved, and the computation of the approximant is much faster: if M is the number of derivatives with respect to x and y, the algorithm requires O(M 4) operations instead of O(M 6) when matrix methods are used for solving the coefficients problem, or O(M 3 ) operations instead of O(M 4) if staircase methods are used. Another important feature is that the reliable methods which have been developed for choosing the degrees of the numerator and the denominator in the univariate case can be straightforwardly used in the multivariate case.

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