|本期目录/Table of Contents|

[1]管钰,丁玖,靳聪明.基于分片线性最大R nyi熵的 Fredholm积分方程数值解法[J].浙江理工大学学报,2022,47-48(自科六):950-958.
 GUAN Yu,DING Jiu,JIN Congming.Numerical solution of Fredholm integral equations via  piecewise linear maximum Rényi entropy method[J].Journal of Zhejiang Sci-Tech University,2022,47-48(自科六):950-958.
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基于分片线性最大R nyi熵的 Fredholm积分方程数值解法()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第47-48卷
期数:
2022年自科第六期
页码:
950-958
栏目:
出版日期:
2022-11-10

文章信息/Info

Title:
Numerical solution of Fredholm integral equations via  piecewise linear maximum Rényi entropy method
文章编号:
1673-3851 (2022) 11-0950-09
作者:
管钰丁玖靳聪明
1.浙江理工大学理学院,杭州 310018;2.南密西西比大学数学系,美国密西西比州哈蒂斯堡 394065045
Author(s):
GUAN Yu DING Jiu JIN Congming
1.School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China; 2.Department of Mathematics, The University of Southern Mississippi, Hattiesburg, MS 39406-5045, USA
关键词:
最大熵原理R nyi熵分片线性基函数Fredholm积分方程数值解法
分类号:
TS195-644
文献标志码:
A
摘要:
大部分积分方程无法求出精确解,因此需考虑数值方法得到近似解。提出了一种基于分片线性基函数的最大R nyi熵的函数恢复方法,证明了解的唯一性,并在此基础上给出基于分片线性最大R nyi熵的Fredholm积分方程数值解法。数值实验表明:基于分片线性最大R nyi熵的Fredholm积分方程数值解法有效,且可以得到比基于分片线性最大Shannon熵的数值解法精度更高的解。

参考文献/References:

1 Jaynes E T. Information theory and statistical mechanics J/OL . Physical Review, 1957, 106: 620-630. https://link.aps.org/doi/10-1103/PhysRev.106-620.

2Mead L R. Approximate solution of Fredholm integral equations by the maximum-entropy methodJ. Journal of Mathematical Physics, 1986, 27(12): 2903-2907.

3Bandyopadhyay K, Bhattacharya A K, Biswas P, et al. Maximum entropy and the problem of moments: A stable algorithmJ. Physical Review E, 2005, 71(5): 057701.

4Ding J, Jin C M, Rhee N H, et al. A maximum entropy method based on piecewise linear functions for the recovery of a stationary density of interval mappingsJ. Journal of Statistical Physics, 2011, 145(6): 1620-1639.

5]张茹,徐春伟,靳聪明.最大熵方法在计算二维不变测度中的应用[J. 浙江理工大学学报(自然科学版), 2017, 37(4): 569-574.

6Jin C M, Ding J. Solving Fredholm integral equations via a piecewise linear maximum entropy methodJ. Journal of Computational and Applied Mathematics, 2016, 304: 130-137.

7Jin C M, Ding J. A maximum entropy method for solving the boundary value problem of second order ordinary differential equationsJ. Journal of Mathematical Physics, 2018, 59(10): 103505.

8Shannon C E. A mathematical theory of communicationJ. Bell System Technical Journal, 1948, 27(3): 379-423.

9R nyi A. On measures of entropy and informationC//Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Berkeley: University of California Press, 1961: 547-562.

10Lenzi E K, Mendes R S, da Silva L R. Statistical mechanics based on Rnyi entropyJ. Physica A: Statistical Mechanics and Its Applications, 2000, 280(3/4): 337-345.

备注/Memo

备注/Memo:
收稿日期: 2022-06-30
网络出版日期:2022-09-14
基金项目: 国家自然科学基金项目(11571314)
作者简介: 管钰(1993-),女,江苏南通人,硕士研究生,主要从事积分方程数值解法的研究
通信作者: 靳聪明,E-mail:jincm@zjst.edu.cn
更新日期/Last Update: 2022-11-07