AAM  >> Vol. 3 No. 2 (May 2014)

    Study on a Generalized Bezout Matrix

  • 全文下载: PDF(382KB) HTML    PP.98-103   DOI: 10.12677/AAM.2014.32015  
  • 下载量: 1,474  浏览量: 5,491   科研立项经费支持


孙井鹏,李海昇,陈 楼:安徽大学数学科学学院,合肥;

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


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。

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.

孙井鹏, 吴化璋, 李海昇, 陈楼. 一类广义Bezout矩阵的研究[J]. 应用数学进展, 2014, 3(2): 98-103. http://dx.doi.org/10.12677/AAM.2014.32015


[1] Barnett, S. (1983) Polynomials and linear control system. Marcel Dekker, New York.
[2] Heinig, G. and Rost, K. (1984) Algebraic methods for toeplitz-like matrices and operators. Operator Theory, 13, Birkhauser, Ba-sel.
[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.
[8] Lancaster, P. and Tismenetsky, M. (1985) The Theory of Matrices. 2nd Edition, Academic Press, London.