Vandermonde方程Hilbert方程及Vandermonde矩阵Hilbert矩阵逆的快速与并行算法

1.引言 众所周知,在并行数值代数研究中,降低矩阵求逆与线性方程组求解并行步是一个相当困难的问题。1976年Csanky证明了上述两问题均可在O(log~2n)并行步内完成,所用处理机台数为O(n~4)。然而能否找到时间步为O(logn)的并行算法,长期以来是人们极为关注的问题之一。对于特殊矩阵及方程的研究更是如此。目前除几个极其特殊的

FAST AND PARALLEL ALGORITHMS FOR SOLUTION OF VANDERMONDE AND HILBERT LINEAR SYSTEMS AND INVERSION OF THEIR COEFFICIENT MATRICES

In this paper, we present some parallel algorithms with time steps O(logn) by n~2 processors for both solution of Vandermonde linear systems and inversion of Vandermonde matrices and for both solution of Hilbert linear systems and inversion of Hilbert matrices. We also show that Hilbert matrices are invertible and arithmetic computational complexity. of inversion of Hilbert matrices is upper and lower bounded by O(n~2), where n is the order of matrices.