Results 271 to 280 of about 54,203 (295)

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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Complex temperature plane zeros in the mean-field approximation

Journal of Statistical Physics, 1986
The authors derive asymptotic expressions for the complex temperature plane zeros of the infinite-range Ising model in the scaling regime. The results also apply to high-dimensional, short-range Ising systems. For the nth zero in a system of N spins, the leading asymptotic result is t/sub n/ varies as (n/N)/sup 1/2/(-1+/-i).
M. L. Glasser, V. Privman, L. S. Schulman   +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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APPROXIMATION CHARACTERIZATION OF CLASSES OF FUNCTIONS ON CONTINUA OF THE COMPLEX PLANE

Mathematics of the USSR-Sbornik, 1986
Let E be a compact connected subset of the plane \({\mathbb{C}}\) with simply connected complement \(D:={\hat {\mathbb{C}}}\setminus E\) and let \(L:=\partial D=\partial E\) their common boundary. Let \(\Phi\) map conformally D onto \(\{| w| >1\}\), \(\Phi (\infty)=\infty\), \(\Phi '(\infty)>0\). Put \[ L_ R:=\{z\in D;\quad | \Phi (z)| =R\}\quad (R>1),
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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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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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Rational approximation in the complex plane using a τ-method and computer algebra

Numerical Algorithms, 1997
The 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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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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On some extremal problems of approximation theory in the complex plane

Ukrainian Mathematical Journal, 2004
In 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, 1978
Abstract This paper is concerned with differential equations of the form d2w/dz2 = {u2f(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 that is not necessarily one-sheeted, and may be bounded or unbounded.
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