Results 191 to 200 of about 5,260,799 (222)

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
openaire   +1 more source

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.
openaire   +2 more sources

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.
openaire   +2 more sources

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}.
openaire   +1 more source

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.
openaire   +1 more source

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
openaire   +1 more source

Chebyshev approximation by Gompertz function

Matematychni Metody Ta Fizyko-Mekhanichni Polya, 2022
P. S. Malachivskyy, L. S. Melnychok, Ya. V. Pizyur   +2 more
openaire   +1 more source

Chebyshev representation for rational functions

Sbornik: Mathematics, 2010
An eective representation is obtained for rational functions all of whose critical points, apart from g 1, are simple and their corresponding critical values lie in a four-element set. Such functions are described using hyperelliptic curves of genus g > 1. The classical Zolotarev fraction arises in this framework for g = 1. Bibliography: 8 titles.
openaire   +1 more source

Chebyshev Polynomials as Basis Functions

2018
In the present chapter some of the important properties of Chebyshev polynomials are described, including their recursion relations, their analytic expressions in terms of the powers of the variable x, where \( -1\le x\le 1\), and the mesh points required for the Gauss–Chebyshev integration expression described in Chap. 3.
George Rawitscher, Victo dos Santos Filho, Thiago Carvalho Peixoto   +2 more
openaire   +1 more source

Chebyshev expansions for Abramowitz functions

Applied Numerical Mathematics, 1992
The Abramowitz functions \(J_ n(x)=\int^ x_ 0 t^ n \exp(-t^ 2- x/t)dt\), \(n\) integer, are evaluated by using Chebyshev expansions. Since these functions satisfy the stable recurrence \[ 2J_ n(x)=(n-1)J_{n- 2}(x)+xJ_{n-3}(x),\quad n=3,4,\dots, \] only the coefficients to 20 decimal places of the expansions for \(J_ 0,J_ 1\) and \(J_ 2\) are given.
openaire   +2 more sources