On Integro Quintic Spline Quasi-interpolation

In order to reconstruct function from the integral values of successive subintervals,a kind of direct construction method is proposed.Firstly,the function values at the knots with six order approximation from the linear combination of the integral values are derived.Secondly,the approximated function values are plugged into the values of linear functional in quintic discrete spline quasi-interpolation operators and so-called integro quintic spline quasi-interpolation is constructed.Finally,the error estimate for approximating higher order derivative is obtained with the benefit of the convergence order of traditional spline quasi-interpolation.Experiments show that our proposed method performs simpler and more effective than traditional integro spline interpolation.Moreover,it can be easily generalized to integro spline quasi-interpolation of higher degree.