数值求积公式在平均框架下的误差分析
发布时间：2018-11-06 18:22
【摘要】：本文得到了复化Simpson公式,Gauss-Legendre求积公式以及基于第二类Chebyshev多项式极值点的数值求积公式在r-重积分Wiener空间下的平均误差.对于复化Simpson公式我们证明了其饱和阶为3.对于Gauss-Legendre求积公式得到它是一种对具有不同光滑性的函数都有高度准确性的通用算子.我们给出了基于第二类Chebyshev多项式极值点的数值求积公式,并在r=0,1,2时给出了逼近误差的强渐近阶.
[Abstract]:In this paper, we obtain the average error of complex Simpson formula, Gauss-Legendre quadrature formula and the numerical quadrature formula based on the extreme point of the second Chebyshev polynomial in the r-multiple integral Wiener space. For the complex Simpson formula, we prove that its saturation order is 3. For the Gauss-Legendre quadrature formula, it is obtained that it is a universal operator with high accuracy for functions with different smoothness. We give a numerical quadrature formula based on the extremum point of the second kind of Chebyshev polynomials, and give the strong asymptotic order of the approximation error at r ~ (0 ~ 0 ~ 1, 2).
【学位授予单位】：天津师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O172.2
本文编号：2315099
[Abstract]:In this paper, we obtain the average error of complex Simpson formula, Gauss-Legendre quadrature formula and the numerical quadrature formula based on the extreme point of the second Chebyshev polynomial in the r-multiple integral Wiener space. For the complex Simpson formula, we prove that its saturation order is 3. For the Gauss-Legendre quadrature formula, it is obtained that it is a universal operator with high accuracy for functions with different smoothness. We give a numerical quadrature formula based on the extremum point of the second kind of Chebyshev polynomials, and give the strong asymptotic order of the approximation error at r ~ (0 ~ 0 ~ 1, 2).
【学位授予单位】：天津师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O172.2
【共引文献】
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