Results 161 to 170 of about 574,412 (205)

Numerical Chebyshev Approximation in the Complex Plane

SIAM Journal on Numerical Analysis, 1972
The paper describes a numerical method for computing rational approximations of analytic functions on arbitrary simply-connected closed regions of the complex plane. The method is based on approximation on finite point sets and can be regarded as a generalization of the exchange algorithm for real rational approximation.
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The approximate solution of nonlinear Fredholm implicit integro-differential equation in the complex plane

Asian-European Journal of Mathematics, 2021
This paper’s purpose is to study the nonlinear Fredholm implicit integro-differential equation in the complex plane, where the term implicit integro-differential means that the derivative of unknown function is founded inside of the integral operator. Initially, according to Banach fixed point theory, we ensure that the equation has a unique solution ...
Lemita, Samir, Touati, Sami, Derbal, Kheireddine   +2 more
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The monopolar rational fractional approximation of the exponent in the complex plane

USSR Computational Mathematics and Mathematical Physics, 1981
Abstract 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, 2015
For \(\alpha>0\), 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, 1979
Reduced 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, 2013
The 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

1988
Let 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, 1970
This 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, 1979
The 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, 2016
Suppose 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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