基于改进正则化蝙蝠算法求解第一类Fredholm积分方程  

An Improved Regularization Bat Algorithm for Solving the First Kind of Fredholm Integral Equation

作　　者：张新明 刘一博 ZHANG Xinming;LIU Yibo(Harbin Institute of Technology(Shenzhen),Shenzhen 518055,China)

机构地区：[1]哈尔滨工业大学(深圳),深圳518055

出　　处：《应用泛函分析学报》2020年第3期141-149,共9页Acta Analysis Functionalis Applicata

基　　金：广东省自然科学基金(2017A030313280)。

摘　　要：本文提出了一种改进正则化蝙蝠算法来求解第一类Fredholm积分方程.对蝙蝠算法的速度惯性系数做出调整以增加种群多样性,添加高斯扰动来进一步优化集群,并采用Tikhonov正则化方法解决不适定性.计算实例表明:改进正则化蝙蝠算法的收敛速度和精度都优于传统正则化蝙蝠算法,并解决了严重偏离点的问题.An improved regularization bat algorithm is proposed for solving the first kind of Fredholm integral equation in this paper.Based on the traditional bat algorithm,the velocity inertia coefficient is adjusted to increase the diversity of population,the Gauss disturbance is added to further optimize cluster,and the Tikhonov regularization method is applied to handle the ill-posedness.The results of numerical simulation show that the convergence speed and numerical precision are better than the regularization bat algorithm.

关 键 词：第一类FREDHOLM积分方程 不适定问题 TIKHONOV正则化 改进蝙蝠算法 

分 类 号：O177.91[理学—数学]