文章主要研究反对称矩阵谱的可信计算. 给定反对称矩阵, 分别利用\,Rump\,区间牛顿法和\,Kantorovich\,定理, 设计算法输出其高精度近似谱和可信误差界. 算法保证在误差界范围内, 存在一反对称矩阵, 该反对称矩阵的精确谱为输出的给定矩阵其高精度近似谱. 算例结果表明, 基于\,Kantorovich\,定理的算法和基于\,Rump\,区间牛顿迭代的算法输出的误差界基本相等.

This paper mainly investigates the verification of the spectra of the skew-symmetric matrix. Given a skew-symmetric matrix, we design two algorithms to compute its high-precision approximate spectra and verified error bound by Rump's interval Newton method and Kantorovich theorem. These algorithms guarantee that there exists a skew-symmetric matrix within computed error bound, whose exact spectra is the computed high-precision approximate spectra of the given matrix. The examples illustrate that the error bounds computed by these two algorithms are equal.