Multivariate Rational Approximants of the PadÉ-Type

1995 ◽  
pp. 221-229
Author(s):  
N. K. Bose
Keyword(s):  
Rational Approximants

Rational approximants generated by the u-transform

1993 ◽  
Vol 78 (1-2) ◽  
pp. 29-54 ◽  
Author(s):  
Dhiranjan Roy ◽  
Ranjan Bhattacharya ◽  
Siddhartha Bhowmick
Keyword(s):  
Rational Approximants

Rational Interpolation of the Exponential Function

1995 ◽  
Vol 47 (6) ◽  
pp. 1121-1147 ◽  
Author(s):  
L. Baratchart ◽  
E. B. Saff ◽  
F. Wielonsky
Keyword(s):  
Rational Function ◽  
Exponential Function ◽  
Complex Plane ◽  
Rational Interpolation ◽  
Real Interval ◽  
Compact Set ◽  
Rational Approximants ◽  
Sharp Estimates ◽  
Image Position ◽  
Uniformly Bounded

AbstractLet m, n be nonnegative integers and B(m+n) be a set of m + n + 1 real interpolation points (not necessarily distinct). Let Rm,n = Pm,n/Qm.n be the unique rational function with deg Pm,n ≤ m, deg Qm,n ≤ n, that interpolates ex in the points of B(m+n). If m = mv, n = nv with mv + nv → ∞, and mv / nv → λ as v → ∞, and the sets B(m+n) are uniformly bounded, we show that locally uniformly in the complex plane C, where the normalization Qm,n(0) = 1 has been imposed. Moreover, for any compact set K ⊂ C we obtain sharp estimates for the error |ez — Rm,n(z)| when z ∈ K. These results generalize properties of the classical Padé approximants. Our convergence theorems also apply to best (real) Lp rational approximants to ex on a finite real interval.

Rational approximants to evaluate four-center electron repulsion integrals for 1s hydrogen Slater type functions

2005 ◽  
Vol 55 (2) ◽  
pp. 173-190 ◽  
Author(s):  
Juan C. Cesco ◽  
Jorge E. Pérez ◽  
Claudia C. Denner ◽  
Graciela O. Giubergia ◽  
Ana E. Rosso
Keyword(s):  
Slater Type ◽  
Rational Approximants ◽  
Electron Repulsion ◽  
Electron Repulsion Integrals
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