Sentence examples for in the approximation of functions from inspiring English sources

Exact(4)

These polynomials present, among others, very good properties in the approximation of functions.

They are widely used because of their good properties in the approximation of functions [18 20].

In addition to computer graphics, the Bernstein polynomials are also used in the approximation of functions, in statistics, in numerical analysis, in p-adic analysis, and in the solution of differential equations.

end{cases} These polynomials are widely used because of their good properties in the approximation of functions and can be determined by the following recurrence formula [22]: begin{aligned} &mathrm{Ch}3_{n+1}(x)=2xmathrm{Ch}3_{n}(x -mathrm{Ch}3_{n-1}(x -mathrm{athrm{Ch}3_{0}(x)=1, &mathrm{Ch}3_{1}(x)=2x-1,qquadn=1,2,ldots.

Similar(56)

In this section, we discuss the approximation of functions with a derivative of bounded variation.

The above mentioned examination inspired us to study further the problem of the approximation of functions in weighted Lipschitz class i.e. (W(L^{r}, xi(t))).

Let C_{2}^{0}[0,infty ):= biggl{ fin C_{2}[0,infty ); lim_{xrightarrow infty }frac{vert f(x) vert }{1+x^{2}} mbox{ exists and is finite} biggr}. Next, we study the approximation of functions in the subspace (C_{2}^{0}[0,infty )) of (C_{2}[0,infty )). Such type of function spaces has been considered by several researchers (cf. [11, 12]).

Several researchers have considered the approximation of functions in this space for different sequences of linear positive operators (cf. [12, 14 16] etc).. Let (f in operatorname{Lip}^_{M}(r)) and (rin 0,1]), then (forall x>0) biglvert L_{n}^{alpha_{n},beta_{n}}(f;x -f(x -figrvert leq M_{f} biggl(frac{delta_{alpha _{n},beta_{n}}(x)}{sqrt{x}} bigrvertr}.

Bernoulli polynomials, first studied by Euler [9], are employed in the integral representation of differentiable periodic functions, and play an important role in the approximation of such functions by means of polynomials [10].

An adaptive Kriging model is established to improve the computational efficiency and numerical accuracy in the approximation of design functions.

end{aligned}In the approximation of a function u(x) on [a, b], in terms of continuous orthogonal polynomials (phi _i(x)), we use the expansion (u(x)=sum _{i=0}^{N}c_{i}phi _i(x)), where the coefficients (u_{i}) are computed by begin{aligned} c_{i}=frac{1}{Vert phi _iVert }int _{a}^b w(x u(x phi _i(x mathrm{d}x.

Show more...

Ludwig, your English writing platform

Write better and faster with AI suggestions while staying true to your unique style.

Student

Used by millions of students, scientific researchers, professional translators and editors from all over the world!

MitStanfordHarvardAustralian Nationa UniversityNanyangOxford

Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak quote

Justyna Jupowicz-Kozak

CEO of Professional Science Editing for Scientists @ prosciediting.com

Get started for free

Unlock your writing potential with Ludwig

Letters

Most frequent sentences: