OBS矩阵和OBS-B矩阵的若干结论

Some results on OBS and OBS-B matrices

目的给出实矩阵实特征值的新定位集,并分析OBS(Ostrowski-Brauer Sparse)矩阵的子直和是否仍是OBS矩阵。方法根据OBS-B(Ostrowski-Brauer Sparse B)矩阵的性质、子直和、OBS矩阵的定义,并结合矩阵非奇异性及不等式的放缩技术进行研究。结果与结论基于OBS-B矩阵给出实矩阵实特征值的一个新定位集,理论分析与数值算例表明所给定位集优于已有文献的结果。同时,给出了OBS矩阵的子直和仍是OBS矩阵的一个简易充分条件,数值算例说明了结果的有效性。

Purposes—To give a new localization set for a real eigenvalue of a real matrix,and analyze whether the subdirect sum of the Ostrowski-Brauer Sparse(OBS)matrix is still an OBS matrix.Methods—The research is conducted according to the properties of the Ostrowski-Brauer Sparse B(OBS-B)matrix,the subdirect sum,the definition of the OBS matrix,the non-singularity of the matrix and the scaling technology of inequalities.Result and Conclusion—Based on the OBS-B matrix,a new localization set for a real eigenvalue of a real matrix is given.The theoretical analysis and numerical examples show that the given set is better than that in the existing literature.Meanwhile,we give a sufficient condition to ensure that the subdirect sum of OBS matrices is also an OBS matrix.Numerical examples are reported to illustrate the obtained results.