• 论文 •

### 连续区间上积分值的二次样条拟插值

1. 1.浙江工商大学统计与数学学院, 杭州 310018; 2. 大连理工大学数学科学学院,大连 116024
• 出版日期:2018-12-25 发布日期:2019-02-22

WU Jinming, SHAN Tingting,ZHU Chungang. Integro Quadratic Spline Quasi-Interpolants[J]. Journal of Systems Science and Mathematical Sciences, 2018, 38(12): 1407-1416.

WU Jinming1 ,SHAN Tingting1 ,ZHU Chungang2

1. 1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018; 2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024
• Online:2018-12-25 Published:2019-02-22

In some practical fields, the usual function values at the interpolated points are not known, whereas the integral values of some successive intervals are given. How to use the integral values of successive intervals to solve function reconstruction is a significant problem. This paper firstly proposes a class of quadratic spline quasi-interpolants from the integral values of successive intervals. It is a direct construction and it is called integro quadratic spline quasi-interpolants. Secondly, we analyze its polynomial reproducing property and give its super convergence property when it approximates the function values at the knots, and so on. Lastly, a type of modified integro quadratic spline quasi-interpolants and its corresponding properties are presented. Experiments show that the proposed quasi-interpolants are simpler and more effective than the existing integro cubic spline quasi-interpolants. Moreover, it can be generalized to integro spline quasi-interpolants with higher degree.

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 [1] 吴金明，单婷婷，朱春钢. 连续区间上积分值的MQ拟插值算子[J]. 系统科学与数学, 2019, 39(12): 1972-1982. [2] 吴金明，张雨，张晓磊，朱春钢. 连续区间上积分值的偶次样条插值[J]. 系统科学与数学, 2017, 37(10): 2085-2094.