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

DOI: 10.12677/AAM.2014.32015, PDF, HTML, 下载: 2,627  浏览: 10,648  科研立项经费支持

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.

 [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.