Rational Approximation to the Exponential Function with Complex Conjugate Interpolation Points
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TL;DR: Different convergence results and precise estimates for the error function in compact sets of C that generalize the classical properties of Pade approximants to the exponential function are obtained.
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About: This article is published in Journal of Approximation Theory. The article was published on 01 Aug 2001. and is currently open access. The article focuses on the topics: Exponential polynomial & Entire function.
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Citations
On pade′ approximations to the exponential function and application to the point kinetics equations
TL;DR: In this paper, a general expression for a special type of functions has been introduced, which allows us to approximate the exponential function in an economical manner, and the different cases of Pade approximation are perturbed so that the resulting approximations have a smaller minimum maximum error on the desired interval especially at large transient time steps.
37
A Rolle's theorem for real exponential polynomials in the complex domain
TL;DR: In this paper, the authors presented a version of Rolle's theorem for real exponential polynomials having a number L sufficiently large of zeros in a compact set K of the complex plane.
29
Riemann-Hilbert analysis and uniform convergence of rational interpolants to the exponential function
TL;DR: From the asymptotic behavior of the polynomials p and q, uniform convergence of general rational interpolants to the exponential function and a precise estimate on the error function is deduced.
17
Full length article: On sequences of rational interpolants of the exponential function with unbounded interpolation points
T. Claeys,Franck Wielonsky +1 more
TL;DR: The local uniform convergence of r"n(z) to e^z in the complex plane, as n tends to infinity, is proved, and it is shown that the limit distributions of the conveniently scaled zeros and poles of R"n are identical to the corresponding distributions ofThe classical Pade approximants.
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•Posted Content
On sequences of rational interpolants of the exponential function with unbounded interpolation points
Tom Claeys,Franck Wielonsky +1 more
TL;DR: In this article, the authors consider sequences of rational interpolants of degree n to the exponential function associated to a triangular scheme of complex points, and prove the local uniform convergence of $r_n(z)$ to $e^{z}$ in the complex plane, as $n$ tends to infinity.
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References
•Book
Geometry of Polynomials
Morris Marden
- 31 Dec 1970
TL;DR: In the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history.
1.4K
•Book
General Orthogonal Polynomials
Herbert Stahl,Vilmos Totik +1 more
- 01 Jan 1992
TL;DR: In this article, the authors consider the zero distribution of orthogonal polynomials and regular n-th root asymptotic behaviour of polynomial polynomorphisms.
567
•Book
Rational Approximation of Real Functions
Pencho Petrushev,Vasil Atanasov Popov +1 more
- 28 Feb 2011
TL;DR: In this paper, the authors present the basic achievements of the subject and discuss some topics from complex rational approximation, including linear approximation, spline approximation, and complex rational approximations.
325
Nonlinear Approximation Theory
Dietrich Braess
TL;DR: Nonlinear approximation theory investigates the approximation of functions by other functions, often with the goal of finding the best approximating function.
313