| 高阶高斯型积分计算机求解算法 |
| |
| 引用本文： | 李炯城,林惜斌,肖恒辉,陈芳炯.高阶高斯型积分计算机求解算法[J].计算机工程与设计,2012,33(5):1871-1875. |
| |
| 作者姓名： | 李炯城 林惜斌 肖恒辉 陈芳炯 |
| |
| 作者单位： | 1. 广东省电信规划设计院有限公司,广东广州510630;广州市无线网络优化重点工程中心,广东广州510630
2. 华南理工大学电子与信息学院,广东广州,510640 |
| |
| 基金项目： | 广东省教育部产学研结合基金项目(2009B090300393);广州市软件(动漫)产业发展资金基金项目(2060404);广东省自然科学基金项目(9351064101000003) |
| |
| 摘 要： | 提出一种新颖的高阶高斯积分算法.该算法不仅可以高效地求解高阶高斯积分问题,而且无论权函数是否为标准正交多项式均能统一处理,因而具有更广泛的工程应用价值和适用性.所提算法通过借助Hankel矩阵高效地解决了与高斯积分相关的非线性方程组的求解问题.算法只涉及矩阵乘法、求逆及求特征值等初等矩阵运算,而传统的方法需要应用到选代搜索等数值方法.因此新的算法具有更高的计算效率和精度.
|
| 关 键 词： | 高阶高斯积分 计算机求积 数值积分 Hankel矩阵 正交多项式 |
Computer algorithm for high-degree Gauss-type quadrature |
| |
| LI Jiong-cheng
,
LIN Xi-bin
,
XIAO Heng-hui
,
CHEN Fang-jiong.Computer algorithm for high-degree Gauss-type quadrature[J].Computer Engineering and Design,2012,33(5):1871-1875. |
| |
| Authors: | LI Jiong-cheng LIN Xi-bin XIAO Heng-hui CHEN Fang-jiong |
| |
| Affiliation: | 1.Guangdong Planning and Designing Institute of Telecommunications Company,Guangzhou 510630,China;2.The Key Center of Wireless Network Optimization of Guangzhou,Guangzhou 510630,China;3.School of Electronics and Information,South China University of Technology,Guangzhou 510640,China) |
| |
| Abstract: | A novel algorithm for high-degree Gauss-type quadrature is proposed,which can not only solve high degree problems,but also solve them in a uniform way,regardless of whether the associated weight functions are standard orthogonal polynomials or not.Thus,the method has a wider range of applications in engineering computing.Using the Hankel matrices,the proposed method can solve the associated non-linear equations efficiently.The method only requires elementary matrix operations such as matrix multiplication,inversion,and computing the eigenvalues,while the traditional methods often use numerical methods such as iteration and searching.Hence,the proposed method is more efficient and accurate. |
| |
| Keywords: | high-degree Gauss-type quadrature computer integration numerical integration Hankel matrix orthogonal polynomials |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
