A review of multivariate Padé approximation theory
✍ Scribed by Annie A.M. Cuyt
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 682 KB
- Volume
- 12-13
- Category
- Article
- ISSN
- 0377-0427
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📜 SIMILAR VOLUMES
A new definition of multivariate Pade approximation is introduced, which is a natural generalization of the univariate Pade approximation and consists in replacing the exact interpolation problem by a least squares interpolation. This new definition allows a straightforward extension of the Montessu
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
We explicitly construct both homogeneous and nonhomogeneous multivariate Pad& approximants to some functions which satisfy some simple functional equations, by using the residue theorem and the functional equation method which has been used successfully by Borwein (1988) to construct one variable Pa
Methods of Padé approximation are used to analyse a multivariate Markov transform which has been recently introduced by the authors. The first main result is a characterization of the rationality of the Markov transform via Hankel determinants. The second main result is a cubature formula for a spec
The notion of partial Padé approximant is generalized to that of general order multivariate partial Newton-Padé approximant. Previously introduced multivariate Padé-type approximants are recaptured as special cases so that it is a true and unifying generalization. The last section contains numerical