最小二乘拟合在积分求解时的应用及程序实现  

Application of least square fitting in integral solution and program implementation

作　　者：刘贯飞 雷胜友[1] 崔舜 LIU Guan-fei;LEI Sheng-you;CUI Shun(School of Highway,Chang'an University,Xi'an 710064,China)

机构地区：[1]长安大学公路学院,陕西西安710064

出　　处：《河南城建学院学报》2019年第1期65-72,共8页Journal of Henan University of Urban Construction

基　　金：国家自然科学基金(59479017)

摘　　要：针对科学研究和工程实践中经常遇到的"不可积"的积分表达式,使用最小二乘拟合进行辅助求解。通过在原被积函数图像上先取点再拟合的办法,将原被积函数替换成一个可积的多项式,进而求出积分的解。根据文中的计算结果,最小二乘曲线或曲面拟合辅助法求出的积分值与数值积分的结果非常接近,而泰勒级数辅助法的结果则与数值积分的结果相差较大。因此,最小二乘拟合作为一种相当精确的积分求解辅助工具,值得在科研和工程领域推广。Aimed at the integral expression with non-integrability encountered in scientific research and engineering,least square fitting is used.Through tracing points on the original integrand image and then fitting,the original integrand function is replaced by an integrable polynomial,and then the solution is obtained.According to the results in the paper,the integral values calculated by least square fitting assisted are closed to the results from numerical integrating,while the results of Taylor series aided are quite different from those of numerical integration.Thus,as a fairly precise integral solving aided tool,least square fitting is worth popularizing in scientific research and engineering.

关 键 词：积分表达式 不可积 曲线拟合 曲面拟合 最小二乘法 

分 类 号：O29[理学—应用数学]