A kind of improved univariate multiquadric quasi-interpolation operators

Abstract

a b s t r a c tIn this paper, a kind of improved univariate multiquadric quasi-interpolation operators is proposed by using Hermite interpolating polynomials. Error analysis shows that the convergence rate of the operators depends heavily on the shape parameter c, which indicates that our operators could provide the desired smoothness and precision by choosing a suitable value of c. Numerical examples show that the operators provide a high degree of accuracy. Moreover, operators are applied to the fitting of discrete solutions of initial value problems.

A new multiquadric quasi‐interpolation operator with interpolation property

“…So we construct a new MQ quasi‐interpolation operator denoted by that is based on RBF interpolation at a given set a relatively small number of interpolated data and quasi‐interpolation operator at another set of relatively large number of approximated data. The most important thing is that does not require any derivative values of f ( x ) at scattered data points compared with the existing operators in .…”

“…Feng and Li constructed a shape‐preserving quasi‐interpolation operator by shifts of cubic MQ functions and proved it can produce an error of as . In 2010, Wang et al proposed a kind of improved univariate MQ quasi‐interpolation operators by using Hermite interpolating polynomials, and the convergence rate depended heavily on the shape parameter c . Jiang et al proposed two new multilevel univariate MQ quasi‐interpolation operators and with higher approximation order.…”

Pointwise and uniform approximation by multivariate neural network operators of the max-product type

“…Note that, the name quasi-interpolation for such kind of operators which in general approximate but do not interpolate functions dened on the whole real space, is typically used in the literature, see e.g., [13,7,41,43,37,30].…”

A kind of multiquadric quasi-interpolation operator satisfying any degree polynomial reproduction property to scattered data

“…Chen et al [8] devised a new multiquadric quasi-interpolation with the properties of linear reproducing and preserving monotonicity. By using Hermite interpolating polynomials, Wang et al [9] proposed a kind of improved univariate multiquadric quasi-interpolation operator, and gave the convergence rate under a certain assumption. The application of multiquadric interpolation or quasiinterpolation may be also found in [10][11][12][13][14].…”