Sentence examples for basis functions of polynomial from inspiring English sources

Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfvén time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger.

The authors established L2 error estimates of the proposed methods and also presented a criterion for the choice of basis functions of the non-polynomial spaces to have the same approximation rates as those of polynomial finite element spaces of the same dimension.

In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees.

Jüttler [7] derived an explicit formula for the dual basis function of Bernstein polynomials.

Alternatively, the monomial basis functions of Volterra filters have also been replaced by Legendre polynomials [49, 50] or Fourier basis functions (sinusoids) [51].

A class of new polynomial basis functions with n − 1 local shape control parameters is presented here to allow the construction of Bézier curves with n local shape control parameters, which is an extension to the classical Bernstein basis functions of degree n.

The computation of Zernike moments comprises three main steps, computing the radial polynomial, computing the basis function of Zernike and computing Zernike moments.

Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses.

In this paper a quad/triangle subdivision surface is expressed analytically as the linear combination of these basis functions and the polynomial reproduction of matrix-valued quad/triangle schemes is studied.

The main idea of all versions of spectral methods is to express the approximate solution of the problem as a finite sum of certain basis functions (orthogonal polynomials or a combination of them) and then choose the coefficients in order to minimize the difference between the exact and approximate solutions as well as possible.

The basic idea of the spectral methods is to express the approximate solution of the problem as a finite sum of certain basis functions (orthogonal polynomials or a combination of them) and then choose the coefficients in order to minimize the residual.