Sentence examples for basis of polynomials with from inspiring English sources

In this paper, we employ the basis of polynomials with degree p that fits the bias field.

Expanding with respect to the basis of the linear space of polynomials with degree at most, we get (33).

A construction of a basis of harmonic polynomials with the above conditions is (2.2).

We used a basis of polynomials up to degree 20 (Λ = 20) to approximate the density of population frequencies.

KLE decomposition was firstly developed to deal with uncertain random field with spatial distribution and the corresponding uncertainties were treated with an orthogonal basis of polynomial chaos (Ghanem and Spanos, 1991).

The parametric influence of operating conditions was then analysed on the basis of polynomial relationships.

Let us consider polynomial p(x) ∈ ℙ n as a linear combination of Bernoulli basis polynomials with p ( x ) = C 0 B 0 ( x ) + C 1 B 1 ( x ) + ⋯ + C n B n ( x ).

We use two different orthonormal bases on VΛ: the basis of Gegenbauer polynomials and the basis of Chebyshev polynomials.

There exist several bases of orthogonal polynomials associated with weights that are high at the boundaries x = 0, 1; however, we chose the basis of Chebyshev polynomials because of the simplicity associated with their implementation.

Analogously, one can write any Chebyshev polynomial C n(x) in the basis of Gegenbauer polynomials as the linear combination C n (x ) = ∑ i = 0 n T i (x ) ∫ 0 1 C n (y ) T i (y ) y (1 − y ) d y, with the coefficients ∫ 0 1 C n (y ) T i (y ) y (1 − y )   d y = 0 for all i > n.

On the basis of quadratic polynomial Eqs.