基于非2π周期三角方法的正常积分模拟与仿真  

Simulation and Emulation of Proper Integrals Based on Non-2π-Periodic Trigonometric Method

作　　者：刘姣[1] 金国祥[1] 

机构地区：[1]武汉工程大学计算机科学与工程学院

出　　处：《武汉工程大学学报》2016年第4期399-403,共5页Journal of Wuhan Institute of Technology

摘　　要：用非周期三角多项式作为逼近工具,对带Chebyshev权的正常积分构造两类求积公式:一类是将带Chebyshev权的正常积分变换成带另一权的正常积分,对后面的积分构造求积公式,然后利用变量逆变换将求积公式变为基于非周期三角多项式的原正常积分的求积公式;另一类是用正常积分的被积函数在非周期三角多项式生成子空间上的正交投影对被积函数进行逼近而得到求积公式;同时提出了这两种求积公式精度的概念.对上述两种求积公式在计算机上用MATLAB编程实现,当被积函数不是周期函数且不均匀时,得到的求积公式逼近效果优于传统意义下的求积公式,实验结果与理论分析相符.We constructed two kinds of quadrature formulae of the proper integral with Chebyshev weight usingthe nonperiodic trigonometric polynomials as the approximate tool.First,we constructed the quadrature fomulaof the integral with a new weight transformed from the integral with Chebyshev weight.And then,we trans-formed it by the inverse transform of the variable to get the first quadrature formula of the original integral basedon the nonperiodic trigonometric polynomials.We obtained the second quadrature formula by using the orthogo-nal projection of the integrand on the subspace spanned by the nonperiodic trigonometric polynomials to approxi-mate the integrand.Meanwhile,we presented the precision conception of the two quadrature formulae.We emu-lated the two kinds of quadrature formulae with MATLAB.The approximation effects of the two quadrature for-mulae are better than those of the quadrature formulae in general when the integrand is nonperiodic and non-uni-form,which consistents with our theoretical analysis.

关 键 词：非周期三角多项式 多项式逼近 求积公式 

分 类 号：O241.38[理学—计算数学] O174.41[理学—数学]