实对称矩阵谱的可信计算

The Verification of the Spectra of the Real Symmetric Matrix

本文主要研究实对称矩阵谱的可信计算。给定实对称矩阵,首先利用Matlab中的eig命令求其数值谱,然后利用Kantorovich定理,设计算法计算数值谱的可信误差界。算法保证在该误差界范围内存在一实对称矩阵,该实对称矩阵的精确谱为给定实对称矩阵的数值谱。

This paper mainly investigates the verification of the spectra of the real symmetric matrix. Given a real symmetric matrix, we firstly use eig code in Matlab to obtain its numerical spectra. Then by Kantorovich theorem, we provide an algorithm to compute verified error bound such that there exists a perturbed real symmetric matrix within computed error bound, whose exact spectra is the computed numerical spectra of the given matrix.