Results 251 to 260 of about 54,457 (295)

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)
Vladimir Andrievskii
exaly   +2 more sources

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 ...
Vladimir V Andrievskii
exaly   +2 more sources

Focal approximation on the complex plane

Computational Mathematics and Mathematical Physics, 2011
Summary: The problem of analytic approximation of a smooth closed curve specified by a set of its points on the complex plane is proposed. An algorithmic method for constructing an approximating lemniscate is proposed and investigated. This method is based on a mapping of the curve to be approximated onto the phase circle; the convergence of the method
exaly   +2 more sources

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