Results 261 to 270 of about 575,074 (283)
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The monopolar rational fractional approximation of the exponent in the complex plane
USSR Computational Mathematics and Mathematical Physics, 1981Abstract The approximation of the exponent in an unbounded left domain of the complex plane by rational fractional functions with one pole is considered.
A.V. Krestinin, B.V. Pavlov
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Polynomial Approximation on Touching Domains in the Complex Plane
Computational Methods and Function Theory, 2015For \(\alpha>0\), consider the ``analytic continuation'' \(f_{\alpha}\) of \(|z|^{\alpha}\) defined by \[ f_{\alpha}(z)=\begin{cases} z^{\alpha}&\text{if }\text{Re}(z)>0,\\ (-z)^{\alpha} &\text{if }\text{Re}(z)
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Model reduction by best Chebyshev rational approximations in the complex plane
International Journal of Control, 1979Reduced order models of high-order single-input single-output dynamical systems are derived in terms of beat Chebyshev rational approximations on a desired domain in the complex plane. An algorithm is proposed for deriving local best Chebyshev rational approximations for a complex function in the complex plane and is based on a complex version of ...
Y. BISTRITZ, G. LANGHOLZ
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Pointwise Copositive Polynomial Approximation on Arcs in the Complex Plane
Computational Methods and Function Theory, 2013The author considers a real-valued function \(f\) which is continuous on a Jordan arc in the complex plane. The paper is devoted to the construction of a sequence of harmonic polynomials copositive with \(f\), while \(f\) changes sign finitely many times, that provides an approximation of \(f\) under additional assumptions of smoothness of the arc in ...
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Remarks on “almost best” Approximation in the Complex Plane
1988Let f(x) be a continuous function on the compact interval J of the real axis, which is not the restriction of a function holomorphic in a neighborhood of J. Let π n be the set of all polynomials over ℂ of degree ≤ n. Let p n (x) be the polynomial of best approximation to f(x) on J, i.e., $$ E_n(f,J)=in f_{q \in {\pi_{n}} } \parallel f-q \parallel J=
J. M. Anderson, W. H. J. Fuchs
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ON APPROXIMATION IN THE MEAN ON CURVES IN THE COMPLEX PLANE BY POLYNOMIALS WITH INTEGER COEFFICIENTS
Mathematics of the USSR-Izvestiya, 1970This work investigates conditions for the possibility of approximating functions f(z) in the pth order mean on a curve C with arbitrary accuracy by polynomials whose coefficients are algebraic integers from a complex quadratic field. The case when f(z) is an analytic function of class Ep in the region bounded by a closed curve C is examined, as is the ...
Al'per, S. Ya., Vinogradova, I. Yu.
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Characterization and Computation of Rational Chebyshev Approximations in the Complex Plane
SIAM Journal on Numerical Analysis, 1979The paper is concerned with the characterization and computation of local best rational Chebyshev approximations to continuous complex-valued functions on subsets of the complex plane. Some numerical examples are presented.
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The problem of approximation in mean on arcs in the complex plane
Mathematical Notes, 2016Suppose that \(\Gamma\) is a rectifiable Jordan curve with diameter \(d\) and let \(E^{(p)}_n(f,\Gamma)\) be the best approximation of a function \(f\,:\;\Gamma\to \mathbb{C}\) by algebraic polynomials of order at most \(n\) in the space \(L^p(\Gamma)\).
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On some extremal problems of approximation theory in the complex plane
Ukrainian Mathematical Journal, 2004In the Hardy Banach spaces Hq, Bergman Banach spaces H′q, and Banach spaces ℬ (p, q, λ), we determine the exact values of the Kolmogorov, Bernstein, Gel’fand, linear, and trigonometric n-widths of classes of functions analytic in the disk |z| < 1 and such that the averaged moduli of continuity of their r-derivatives are majorized by a certain function.
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General connection formulae for Liouville-Green approximations in the complex plane
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1978This paper is concerned with differential equations of the form d 2 w/dz 2 = {u 2 f(u,z) +g(u,z)}w in which u is a positive parameter and z is a complex variable ranging over a simply connected open domain D
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