Sentence examples for basis functions are given from inspiring English sources

Some interesting properties of the basis functions are given.

Next, we show that the optimal non-overlapping basis functions in the minimal mean square error sense can be found by solving an eigenvalue problem without numerical search when the feasible overlapping basis functions are given.

where the Baskakov and beta basis functions are given in (1).

In this section, some preliminaries and notations related to fractional calculus and sinc basis functions are given.

The procedure for modifying the basis functions is given as follows: B ˜ 0 x = B 0 x + 2 B − 1 x Open image in new window B ˜ 1 x = B 1 x − B − 1 x Open image in new window B ˜ j x = B j x, j = 2, …, N − 2 Open image in new window (3.1) B ˜ N − 1 x = B N − 1 x − B N + 1 x Open image in new window B ˜ N x = B N x + 2 B N + 1 x Open image in new window.

The closed-form expression of the basis functions is given in the Supplementary Information.

The two-scale equations for scaling and wavelet basis function are given as follows: (3) φ t = 2 ∑ m ∈ Z h m φ 2 t − m, (4) ψ t = 2 ∑ m ∈ Z g m φ 2 t − m, where g m = (−1) m h1− m.

The quintic B-spline basis function is given in Sect. 2. The finite difference approximation for time discretization of the given problem is discussed in Sect.

Note that the weight of each basis function is given by the corresponding coefficient in w i, and the estimated w i is sparse.

Recently, spectral method were developed to solve partial fractional differential equations in which the choice of the basis function is given by means of Jacobi polynomials; see [30, 31].

Within the space time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space time nodes.