𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Convergence of the Nested Multivariate Padé Approximants

✍ Scribed by Philippe Guillaume

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
303 KB
Volume
94
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

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 only involves univariate Pade approximation. This allows us to obtain uniform convergence where the classical multivariate Pade approximants fail to converge.

📜 SIMILAR VOLUMES

On the Convergence of General Order Mult
On the Convergence of General Order Multivariate Padé-Type Approximants
✍ J. Abouir; A. Cuyt; P. Gonzalez-Vera; R. Orive 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 474 KB

In previous papers the convergence of sequences of ``rectangular'' multivariate Pade -type approximants was studied. In other publications definitions of ``triangular'' multivariate Pade -type approximants were given. We extend these results to the general order definition where the choice of the de

Convergence Rates of Padé and Padé-Type
Convergence Rates of Padé and Padé-Type Approximants
✍ Amiran Ambroladze; Hans Wallin 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 356 KB

A comparison is made between Pade and Pade -type approximants. Let Q n be the n th orthonormal polynomial with respect to a positive measure + with compact support in C. We show that for functions of the form where w is an analytic function on the support of +, Pade -type approximants with denomina

Generalized Multivariate Padé Approximan
Generalized Multivariate Padé Approximants
✍ Philippe Guillaume; Alain Huard; Vincent Robin 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 328 KB

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

Multivariate Partial Newton-Padé and New
Multivariate Partial Newton-Padé and Newton-Padé Type Approximants
✍ J. Abouir; A. Cuyt 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 418 KB

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

Convergence Properties Related to p-Poin
Convergence Properties Related to p-Point Padé Approximants of Stieltjes Transforms
✍ O. Njastad 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 377 KB

Let \(\psi\) be a finite positive measure on \(\mathbf{R}\), and let \(F_{\psi}(z)=\int_{-x}^{x}(d \psi(t) /(z-t))\) be its Stieltjes transform. A special multipoint Padé approximation problem for \(F_{\psi}(z)\) is studied, where the interpolation points are a finite number of points \(a_{1}, \ldot