Vol.3 No.02(2014), Article ID:13570,5 pages DOI:10.12677/AAM.2014.32015

Jingpeng Sun1, Huazhang Wu1,2*, Haisheng Li1, Lou Chen1

1School of Mathematical Sciences, Anhui University, Hefei

2Key Laboratory of Intelligent Computing and Signal Processing, Ministry of Education, Anhui University, Hefei

Email: 1946179973@qq.com, *wuhz@ahu.edu.cn

Received: Mar. 20th, 2014; revised: Apr. 17th, 2014; accepted: Apr. 24th, 2014

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.

Keywords:Bilinear Transformation Function, Polynomial Basis, Bezout Matrix, Triangular Decomposition

1安徽大学数学科学学院，合肥

2安徽大学教育部智能计算与信号过程重点实验室，合肥

Email: 1946179973@qq.com, *wuhz@ahu.edu.cn

1. 引言

2. 广义Bezout矩阵元素的计算

, (1)

(2)

(3)

(4)

,。则基的第项多项

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.

.

.

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3. Barnett, S. and Lancaster, P. (1980) Some properties of the Bezoutian for polynomial matrices. Linear and Multilinear Algebra, 9, 99-110.

4. Mani, J. and Hartwig, R.E. (1997) Generalized polynomial bases and the Bezoutian. Linear Algebra and Its Applications, 251, 293-320.

5. Wu, H.Z. (2010) More on polynomial Bezoutians with respect to a general basis. Electronic Journal of Linear Algebra, 21, 154-171.

6. Yang, Z.H. and Hu, Y.J. (2004) A generalized Bezoutian matrix with respect to a polynomial sequence of interpolatory type. IEEE Transactions on Automatic Control, 49, 1783-1789.

7. Bini, D.A. and Gemignani, L. (2004) Bernstein-Bezoutian matrices. Theoretical Computer Science, 315, 319-333.

NOTES

*通讯作者。