利用区间算法, 研究结构矩阵秩亏的可信性验证. 给定具有特殊代数结构且数值秩为$k$的实矩阵$A(\text{bm}p)$, 给出算法输出具有相同代数结构的区间矩阵$A(\text{bm}p+\text{bm}W)$, 其每一个位置的元素为矩阵$A(\text{bm}p)$相应位置的元素的很小的区间摄动, 使得区间矩阵$A(\text{bm}p+\text{bm}W)$ 中包含一具有相同代数结构且秩为$k$的实矩阵$A(\bm{p}+\widehat{\bm{w}}

This paper mainly discusses the certification of the structure matrix with rank deficiency using interval algorithm. For a structure matrix $A(\text{bm}p)$ with numerical rank $k$, this paper gives an algorithm which outputs an interval matrix $A(\text{bm}p+\text{bm}W)$ with the same algebraic structure such that $A(\text{bm}p+\text{bm}W)$ contains a real matrix $A(\text{bm}p+\widehat{\text{bm}w})$ with the same algebraic structure and rank $k$ within certain error bounds. Specially, each element of $A(\text{bm}p+\text{bm}W)$ is a small interval perturbation of the corresponding element of $A(\text{bm}p)$.