Results 261 to 270 of about 217,177 (294)

Asymptotic Two-Point Approximations by Rational Function

Results in Mathematics, 1997
For every function \(f(s)\) continuous in \(0\leq s\leq \infty\) possessing asymptotic power expansions both for \(s\to +0\) and for \(s\to+\infty\), the author in the paper under review proves the existence of a sequence of rational functions \(r_n(s)\) with positive denominators satisfying the property \(r_n(s)- f(s)= \begin{cases} O(s^n) \quad ...
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Approximation by Bernstein type rational functions. II

Acta Mathematica Academiae Scientiarum Hungaricae, 1982
The authors consider the discrete linear operator \[ R_ n(f,x)=\frac{1}{(1+a_ nx)^ n}\sum^{n}_{k=0}f(f/b_ n)\binom{n}{k}\;(a_ nx)^ k \] in the special case \(a_ n=^{\beta - 1}\), \(b_ n=n^{\beta ...
Balázs, Catherine, Szabados, Jozsef
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Best Uniform Rational Approximations of Functions by Orthoprojections

Mathematical Notes, 2004
Let \(X\) be one of the following Banach spaces: \(C[- 1, 1]\), the space of complex continuous functions on the interval \([-1,1]\); \(C(\mathbb T)\), the space of complex continuous functions on the circle \(\mathbb T = \{z :| z| = 1\}\); and \(C_A\), the space of functions analytic in the disk \(\mathbb D = \{z :| z| < 1\}\) and continuous on its ...
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Black-box modelling by rational function approximation

Proceedings. 45th Annual IEEE Symposium on Foundations of Computer Science, 2005
In this paper, a rational function approach is used to approximate the transfer function of linear systems characterized by sampled data. The ill-conditioned Vandermonde-like matrix associated with the ordinary power series is avoided by using Chebyshev polynomials.
null Rong Gao, Y.S. Mekonnen, W.T. Beyene, J.E. Schutt-Aine   +3 more
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Approximation by generalized Balazs type rational functions

2003
The authors define rational functions connected with Baskakov operators and prove convergence theorems for them. They prove an asymptotic approximation theorem and show that the derivative of generalized Balazs type rational functions also converge to the derivative of the function.
İSPİR, NURHAYAT, ATAKUT, ÇİĞDEM
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Uniform approximation of continuous functions by rational functions

Annali di Matematica Pura ed Applicata, 1970
Viene data la condizione necessaria e sufficiente perche le funzioni razionali di una variabile, aventi poli di ordine prefissato in assegnati punti del piano complesso, costituiscano un sistema completo iu Co (0, 1).
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Comonotone approximation of \(|X|\) by rational functions

1983
It is shown that the rational approximant r(x)\(\in {\mathcal R}^ n_ n[- 1,1]\) introduced by Newman satisfying \(| | x| -r(x)| \leq 3\bar e^{\sqrt{n}}\) is actually a comonotone approximation of \(| x|\) on [-1,1] in that r'(x)\(\leq 0\) for \(x\in [-1,0]\) and r'(x)\(\geq 0\) for \(x\in [0,1]\). Furthermore, it is shown that the result of Vyaceslavov
Iliev, G. L., Optiz, U.
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Approximation of Poincaré's new functions by rational functions

Journal of Difference Equations and Applications, 2013
In this paper, we introduce a way to approximate meromorphic functions belonging to Poincare's ‘new’ class by rational functions. The class consists of meromorphic functions having a ‘theorem de multiplication’ with a suitable condition, which is a system of difference equations on the transform sending to , where . Since graphing rational functions is
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Approximation in the mean by rational functions

Integral Equations and Operator Theory, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Approximation by rational functions in complex regions

Mathematical Notes of the Academy of Sciences of the USSR, 1971
Approximation by rational functions Rn (z) (in the C and Lp metrics) on plane compacta is investigated. The possibility is studied of the coincidence of rational and polynomial approximations for all n, and some functions are described for which this coincidence holds.
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