G-L分数导数高阶逼近算法的鲁比希生成函数系数的求解
Solving the coefficients of Lubich generating function in the algorithm for G-L fractional derivative with high-order approximation
杨紫怡 1袁晓1
作者信息
- 1. 四川大学电子信息学院, 成都 610065
- 折叠
摘要
考察G-L分数导数的逼近阶,引出高精度的数值算法,提出三种求解鲁比希高阶逼近生成函数系数的方法.从信号处理的角度出发,采用拉格朗日插值逼近法首次在理论上严格推导出鲁比希生成函数系数的解析表达式.构造了任意阶次的生成函数,通过不同形式的生成函数等价,用数学归纳和矩阵方程两种方法对生成函数系数进行求解,验证了结果的正确性.
Abstract
Researching the approximation order of G-L fractional derivative,the numerical algorithm with high precision is introduced,and three methods are proposed to solve the coefficients of Lubich generating function with high-order approximation.From the point of view of signal processing,the analytical expression of the coefficients of Lubich generating function is derived strictly theoretically for the first time by using the Lagrange interpolation approximation method.A generating function of any order is constructed.Through the equivalence of different forms of generating function,the coefficients of generating function are solved by mathematical induction and matrix equation,and the correctness of the conclusion is verified.
关键词
分数导数/高阶逼近/鲁比希生成函数/拉格朗日插值逼近/数值算法Key words
Fractional derivative/High-order approximation/Lubich generating function/Lagrange interpo-lation approximation/Numerical algorithm引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据