Multivariate Padé Approximants Associated with Functional Relations
✍ Scribed by Ping Zhou
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 591 KB
- Volume
- 93
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
✦ Synopsis
We explicitly construct non-homogeneous multivariate Pade approximants to some functions like
q &(i+ j) 2 Â2 x i y j , and E(x, y) := : i, j=0
x i y j [i+ j] q ! , which satisfy some functional equations, where |q|>1, q # C.
📜 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
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
We investigate the polynomials P n , Q m , and R s , having degrees n, m, and s, respectively, with P n monic, that solve the approximation problem We give a connection between the coefficients of each of the polynomials P n , Q m , and R s and certain hypergeometric functions, which leads to a sim
The nested multivariate Pade approximants were recently introduced. In the case of two variables x and y, they consist in applying the Pade approximation with respect to y to the coefficients of the Pade approximation with respect to x. The principal advantage of the method is that the computation o