A kind of bivariate Bernoulli-type multiquadric quasi-interpolation operator with higher approximation order

Abstract

In this paper, a kind of bivariate Bernoulli-type multiquadric quasi-interpolation operator is studied by combining the known multiquadric quasi-interpolation operator with the generalized Taylor polynomial as the expansion in the bivariate Bernoulli polynomials. Some error bounds and convergence rates of the combined operators are studied. A selection of numerical examples is presented to compare the performances of the obtained scheme. Furthermore, our method can be applied to time-dependent differential equations. Its advantage is that the algorithm is very simple and easy to implement.

A Kalman Filtering Algorithm for Measurement Interruption Based on Polynomial Interpolation and Taylor Expansion

“…By interpolating a polynomial to a given set of points, a simple and easy-to-compute function is constructed to approximate the objective function, and then the function value of the objective function at a point can be approximated by the function value of the interpolated approximation function at this point. That is, a function f is first obtained as a function of values at certain points in the interval , and then a function p is derived from these values by interpolation such that p and f are very similar [ 23 , 24 , 25 , 26 ].…”