多层积分值三次样条拟插值

发布时间：2018-12-20 15:16

【摘要】：目的在实际问题中,某些插值问题结点处的函数值往往是未知的,而仅仅知道一些连续等距区间上的积分值。为此提出了一种基于未知函数在连续等距区间上的积分值和多层样条拟插值技术来解决函数重构。该方法称之为多层积分值三次样条拟插值方法。方法首先,利用积分值的线性组合来逼近结点处的函数值;然后,利用传统的三次B—样条拟插值和相应的误差函数来实现多层三次样条拟插值;最后,给出两层积分值三次样条拟插值算子的多项式再生性和误差估计。结果选取无穷次可微函数对多层积分值三次样条拟插值方法和已有的积分值三次样条拟插值方法进行对比分析。数值实验印证了本文方法在逼近误差和数值收敛阶均稍占优。结论本文多层三次样条拟插值函数能够在整体上很好的逼近原始函数,一阶和二阶导函数。本文方法较之于已有的积分值三次样条拟插值方法具有更好的逼近误差和数值收敛阶。该方法对连续等距区间上积分值的函数重构具有普适性。
[Abstract]:Aim in practical problems, the function values at the nodes of some interpolation problems are often unknown, but only the integral values on the continuous equidistant intervals are known. Based on the integral value of unknown function in the interval of continuous equidistant and the technique of multilayer spline quasi interpolation, this paper presents a method to solve the problem of function reconstruction. This method is called multilayer integral value cubic spline quasi-interpolation method. Firstly, the linear combination of the integral values is used to approximate the function values at the nodes, then, the traditional cubic B-spline quasi interpolation and the corresponding error functions are used to realize the multilayer cubic spline quasi interpolation. Finally, the polynomial reproduction and error estimation of the cubic spline quasi-interpolation operator with two-layer integral value are given. Results the infinitely differentiable function is chosen to compare the multilayer integral value cubic spline quasi interpolation method and the existing integral value cubic spline quasi interpolation method. Numerical experiments show that the approximation error and numerical convergence order of the proposed method are slightly superior. Conclusion in this paper, the multilayer cubic spline quasi interpolation function can approach the original function, first order and second order derivative function well on the whole. The proposed method has better approximation error and numerical convergence order than the existing integral value cubic spline quasi-interpolation method. This method is universal for the function reconstruction of integral values on the continuous equidistant interval.
【作者单位】：浙江工商大学数学系;大连理工大学数学科学学院;
【基金】：国家自然科学基金项目(11401526,11271328,11671068) 浙江省自然科学基金项目(LY14A010001)~~
【分类号】：O241.3

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