结构方阵秩亏为k的可信性验证

Certification of the Square Structure Matrix with Rank Deficiency k

利用区间算法研究结构矩阵秩亏为k的可信性验证.对具有特殊代数结构的矩阵A(p),给出了算法输出具有相同代数结构的区间矩阵A(p+W),其每个位置的元素为矩阵A(p)相应位置元素的很小区间摄动,使得区间矩阵A(p+W)中包含一个具有相同代数结构且秩亏为k的矩阵A(p+w).结果表明,结构矩阵秩亏为k的可信性验证可以应用到多项式因式分解的可信性计算中.

The authors mainly discussed the certification of the square structure matrix with rank deficiency k.For a square structure matrix A（p）,we gave an algorithm which outputs an interval square matrix A（p＋W）with the same algebraic structure such that A（p＋W）contains a structure matrix A（p＋w）with rank deficiency k,where each element of A（p＋W）is a small interval perturbation of the corresponding element of A（p）.