Rational Function Approximation for Fractional Order Differential and Integral Operators
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摘要: 基于有理函数逼近理论, 提出了一种分数阶微积分算子s域最佳有理逼近函数的构造方法. 详细讨论了构造最佳有理逼近函数的思路、方法及具体算法. 运用最佳有理逼近定义及特征定理, 对所构造的分数阶积分算子最佳有理逼近函数进行了验证. 其结果表明:该分数阶微积分算子最佳有理逼近函数构造方法是有效的, 且对确定的逼近误差及逼近频带, 所构造的最佳有理逼近函数能够以最低阶次取得最佳逼近特性.Abstract: A method of constructing the best rational approximation function is proposed based on rational approximation theory for fractional order differential and integral operators in s domain. The idea, method, and algorithm of constructing the best rational approximation function are discussed in detail. The best rational approximation function constructed for fractional integral operator is tested and verified by using best rational approximation definition and characteristic theorem. The verification results show that the proposed method is efficient, and the best rational approximation function constructed can achieve the best approximation performance with the lowest order for a given approximation error and an interested frequency band.
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