一类广义Bezout矩阵的研究
Study on a Generalized Bezout Matrix

作者: 孙井鹏 , 李海昇 , 陈 楼 :安徽大学数学科学学院,合肥; 吴化璋 :安徽大学数学科学学院,合肥;安徽大学教育部智能计算与信号过程重点实验室,合肥;

关键词: 双线性变换函数多项式基Bezout矩阵三角分解Bilinear Transformation Function Polynomial Basis Bezout Matrix Triangular Decomposition

摘要:

本文通过双线性变换函数构造多项式空间的两个基 ,分两种情形研究在该多项式基下的一类广义Bezout矩阵。通过Bezout矩阵的生成函数给出该矩阵元素的一个快速计算公式和对应的三角分解公式,该计算公式所需工作量为。讨论了两个不同基的广义Bezout矩阵之间的联系。最后,举两个数值例子进行验证。

Abstract: The bases of the polynomial linear space are constructed by the bilinear transformation function. Generalized Bezout matrices under two different bases are investigated. By the generating functions of Bezout matrices, a fast algorithm formula and its corresponding triangular decomposition for the elements of this type of Bezout matrix are given. The formula shows that the cost of the algorithm is . Connection between two Bezout matrices under different bases is discussed. Finally, two numerical examples are given to demonstrate the validity of the theory.

文章引用: 孙井鹏 , 吴化璋 , 李海昇 , 陈 楼 (2014) 一类广义Bezout矩阵的研究。 应用数学进展, 3, 98-103. doi: 10.12677/AAM.2014.32015

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