Hankel矩阵和Vandermonde矩阵之逆的新矩阵表示式及快速算法

New expressions and fast algorithms for inverse of Hankel matrix and Vandermonde matrix

利用线性方程组是否有解给出Hankel矩阵、Vandermonde矩阵可逆的条件及求逆的递推公式,并给出了逆矩阵新的表示式.表明Hankel矩阵、Vandermonde矩阵的逆矩阵可以表示为一些特殊矩阵的乘积之和,并以Hankel矩阵为例,得到了求逆的快速算法,所需计算量为O(n2),一般n阶矩阵求逆的计算量为O(n3).

The Hankel(Vandermonde)matrix is invertible if systems of Hankel(Vandermonde)equations are solvable. Also, the inversion of a Hankel(Vandermonde)matrix can be denoted as a sum of products of particular matrices. Especially, a fast algorithm for the inversion of a Hankel matrix with O( n^2) operations (rather than O(n^3), as required by standard matrix inversion methods) is derived.