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Rational approximation in the complex plane using a τ-method and computer algebra
Numerical Algorithms, 1997The Cauchy problem for systems of linear ordinary differential equations with polynomial coefficients on the complex plane is treated. An adapted Lanczos \(\tau\)-method is derived for global rational approximation of the solution. The method is based on the properties of the Chebyshev series and symbolic computation. Examples are given.
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International Journal of Applied and Computational Mathematics, 2017
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Uniform polynomial approximation of entire functions on arbitrary compact sets in the complex plane
Mathematical Notes, 1995The author considers the connection between the rate of growth of an entire function and the rate of the best polynomial approximation to this function. Let \(K\) be a compact subset on the complex plane. If \(u_1, \dots, u_n \in K\), \(n \in \mathbb{N}\), then set \[ V(u_1, \dots, u_n) = \prod_{1 \leq k < l \leq n} (u_k - u_l), \quad V_n = \max_{u_1, \
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2000
Oscillations in a complex system such as a neuron or an area of cortex imply that recursive exchanges of ions and energy are taking place. Dynamic modeling starts with writing two coupled differential equations having at least two state variables, the output of each equation providing input to the other. These relations describe a feedback loop. One of
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Oscillations in a complex system such as a neuron or an area of cortex imply that recursive exchanges of ions and energy are taking place. Dynamic modeling starts with writing two coupled differential equations having at least two state variables, the output of each equation providing input to the other. These relations describe a feedback loop. One of
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Rational Approximations in the Complex Plane
Journal of the London Mathematical Society, 1955openaire +1 more source
Rational approximation with varying weights in the complex plane
Computational Methods and Function Theory 1997, 1999Igor E. Pritsker, Richard S. Varga
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Rational Approximations in the Complex Plane (II)
Journal of the London Mathematical Society, 1956openaire +2 more sources
2016
In this chapter, firstly for q > 1 the exact order near to the best approximation, \(\frac{1} {q^{n}}\), is obtained in approximation by complex q-Favard–Szasz–Mirakjan, q-Szasz–Kantorovich operators and q-Baskakov operators attached to functions of exponential growth conditions, which are entire functions or analytic functions defined only in compact ...
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In this chapter, firstly for q > 1 the exact order near to the best approximation, \(\frac{1} {q^{n}}\), is obtained in approximation by complex q-Favard–Szasz–Mirakjan, q-Szasz–Kantorovich operators and q-Baskakov operators attached to functions of exponential growth conditions, which are entire functions or analytic functions defined only in compact ...
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Journal of Business and Economic Research
This study successfully applies the Complex Fourier Series to approximate the closed contour of the Luckin Coffee logo, modeled as a periodic function in the complex plane. The methodology leverages the interpretation of complex numbers as rotation vectors.
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This study successfully applies the Complex Fourier Series to approximate the closed contour of the Luckin Coffee logo, modeled as a periodic function in the complex plane. The methodology leverages the interpretation of complex numbers as rotation vectors.
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Pointwise Estimation of Sign-Preserving Polynomial Approximations on Arcs in the Complex Plane
Ukrainian Mathematical Journal, 2022openaire +1 more source