基于二次假设的数值二阶偏导数计算式  

Calculation Expression of Numerical Second-order Partial Deriva tive Based on Quadratic Hypothesis

作　　者：李春明[1,2] 尹晓丽[1,2] 刘庆[1] LI Chun-ming;YIN Xiao-li;LIU Qing(Shengli College in China University of Petroleum,China University of Petroleum(East China),Dongying Shandong 257061,China;School of Mechanical and Electrical Engineering,China University of Petroleum(East China),Qingdao Shandong 266580,China)

机构地区：[1]中国石油大学(华东)中国石油大学胜利学院,山东东营257061 [2]中国石油大学(华东)机电工程学院,山东青岛266580

出　　处：《德州学院学报》2020年第4期15-20,共6页Journal of Dezhou University

基　　金：中国石油大学胜利学院教改基金项目(JG201725);山东省自然科学基金项目(Q2006A08).

摘　　要：在控制、智能、优化、自动化等研究领域,函数的偏导数往往需要由数值方法获得,二阶混合偏导数是制约数值算法的瓶颈.假设该函数为二次函数,详细推导了一阶和二阶数值偏导数及方向导数的数值计算式.基于方向导数的定义式及数值计算式,获得了求解混合偏导数的方程.在两个变量所确定的平面内,以研究点为中心取五个点,基于该方程详细推导出了两个变量之间的二阶混合偏导数数值计算公式.以二维Rosenbrock函数为例验证了所推导计算式的正确性.In the researching fields of control,intelligence,optimization,automation and so on,the partial derivatives of functions are often obtained by numerical methods.The second-order mixed partial derivatives are the bottleneck of numerical algorithms.Assuming that this function is quadratic,the numerical calculation expressions of the first and second numerical partial derivatives and directional derivatives are derived in detail.Based on the definition and numerical calculation of directional derivative,the equation for solving mixed partial derivative is obtained.In the plane determined by the two variables,five points are taken around the study point.Based on the above equation,the numerical calculation formula of the second mixed partial derivative between the two variables is derived in detail.The two-dimensional Rosenbrock function is taken as an example to verify the calculations.All of the derived calculation are correct.

关 键 词：模式识别与信号处理 优化方法 数值微分算法 二阶混合偏导数 方向导数 

分 类 号：O241.4[理学—计算数学] O224[理学—数学]