双线性变换函数生成基下的结式矩阵和Bezout矩阵（英文）

Resultant matrices and Bezoutians under the polynomial bases generated by a bilinear transformation function

通过双线性变换函数构造多项式空间C_(n+1)[z]的两个基{α_i^(n)(z)=(1±z)n-i(1■z)~i,0≤i≤n},对在该基下的结式矩阵和广义Bezout矩阵进行研究.根据结式矩阵可计算两个多项式的最大公因式.给出n阶广义Bezout矩阵元素的两个快速计算公式,计算的工作为o(n^2).最后,对这两类矩阵之间的相互联系进行了讨论.

The bases {α_i^（n）（z）=（1±z）n-i（1干z）~i,0≤i≤n} of linear polynomial space Cn＋l [z] were constructed from a bilinear transformation function. The resultant matrices and generalized Bezoutians for polynomials under such bases were investigated. The greatest common divisor of two polynomials were computed in terms of the resultant matrices. Two fast algorithm formulas for the elements of generalized Bezoutians of order n were given, and the costs of the algorithms were o（nZ）. Connections between these two classes of matrices were were also discussed.