Results 161 to 170 of about 22,208 (203)

Chebyshev Approximation and Threshold Functions

IEEE Transactions on Electronic Computers, 1965
Where previous authors have considered linear approximations with a minimum sum of squared differences, we consider, instead, Chehyshev linear approximations, which minimize the maximum deviation. We obtain thus: 1) A new characterization of threshold functions, 2) A characterization of optimal threshold realizations as being virtually identical to the
Kaplan, K. R., Winder, R. O.
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Generalised chebyshev basis functions

International Journal of Computer Mathematics, 1999
The construction of generalised Chebyshev basis functions in one dimension is carried out for both linear and quadratic cases. The optimal selection of the point of reflection of the required Chebyshev Polynomial (s) is identified.
M. A. Ibiejugba, D. J. Evans, O. M. Bamig-Bola, M. R. Odekunle   +3 more
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Chebyshev subspaces of vector-valued functions

Mathematical Notes of the Academy of Sciences of the USSR, 1976
It is shown that if on a compact space Q any polynomial\(P_N (z) = \sum\nolimits_1^N {\alpha _i } \left( {\begin{array}{*{20}c} {f_{i1} } \\ \vdots \\ {f_{is} } \\ \end{array} } \right),\sum\nolimits_1^N {|\alpha _i |^z > 0} \), in a system of continuous vector functions with real coefficients such that N=n·s and s=2p +1 has at most n−1 zeros, then Q ...
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Algorithm 414: Chebyshev approximation of continuous functions by a Chebyshev system of functions

Communications of the ACM, 1971
The second algorithm of Remez can be used to compute the minimax approximation to a function, ƒ( x ), by a linear combination of functions, { Q i ( x )} n 0 ...
G. H. Golub, L. B. Smith
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On Weight Functions Admitting Chebyshev Quadrature

Mathematics of Computation, 1987
In this paper we prove the existence of Chebyshev quadrature for three new weight functions which are quite different from the two known examples given by Ullman [15] and Byrd and Stalla [2]. In particular, we indicate a simple method to construct weight functions for which there exist infinitely many Chebyshev quadrature rules.
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Chebyshev–Padé approximants for multivalued functions

Transactions of the Moscow Mathematical Society
The paper discusses the connection between the linear Chebyshev–Padé approximants for an analytic function f f and diagonal type I Hermite–Padé polynomials for the set of functions [ 1 , f 1 , f 2 ] [1, f_1, f_2] , where ...
Rakhmanov, E. A., Suetin, S. P.
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On the Chebyshev Function ψ(x)

Lithuanian Mathematical Journal, 2003
Let \(\psi(x)=\sum_{n \leq x}\Lambda(n)\), where \(\Lambda(n)\) is the von Mangoldt function. The author proves that, for \(n\geq2\), \(01\) and assuming the Riemann Hypothesis, \[ \int_1^{T^\beta}\Big| \psi\Big(x+{x\over T}\Big)-\psi(x)-{x\over T}\Big| ^n{dx\over x^{n/2+1}}\ll_{n,\beta}{\beta^n\over n}{\log^nT\over T}.
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Rational chebyshev approximations of elementary functions

BIT, 1961
Explicit formulae which should be useful in practical computations, are given for the functions e−x, log x, Γ(1 + x), arctg x/x, sin x/x, cos x and (2/x) arcsin (x/2) in the interval 0≤x≤1 except for log x, where the interval is 1/2≤x≤1 instead.
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Chebyshev Approximation of Functions of Several Variables

Cybernetics and Systems Analysis, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Malachivskyy, P. S., Pizyur, Ya. V., Malachivskyi, R. P., Ukhanska, O. M.   +3 more
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Chebyshev approximation by Gompertz function

Matematychni Metody Ta Fizyko-Mekhanichni Polya, 2022
P. S. Malachivskyy, L. S. Melnychok, Ya. V. Pizyur   +2 more
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