Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4640265 | Journal of Computational and Applied Mathematics | 2011 | 13 Pages |
In this paper, by virtue of using the linear combinations of the shifts of f(x)f(x) to approximate the derivatives of f(x)f(x) and Waldron’s superposition idea (2009), we modify a multiquadric quasi-interpolation with the property of linear reproducing to scattered data on one-dimensional space, such that a kind of quasi-interpolation operator Lr+1fLr+1f has the property of r+1r+1(r∈Z,r≥0r∈Z,r≥0) degree polynomial reproducing and converges up to a rate of r+2r+2. There is no demand for the derivatives of ff in the proposed quasi-interpolation Lr+1fLr+1f, so it does not increase the orders of smoothness of ff. Finally, some numerical experiments are shown to compare the approximation capacity of our quasi-interpolation operators with that of Wu–Schaback’s quasi-interpolation scheme and Feng–Li’s quasi-interpolation scheme.