Companion矩阵的伪谱问题  

Pseudospectra of companion matrix

作　　者：张敏[1] 王正盛[1] 徐贵力[2] 

机构地区：[1]南京航空航天大学理学院,江苏南京211106 [2]南京航空航天大学自动化学院,江苏南京211106

出　　处：《江苏师范大学学报（自然科学版）》2017年第2期49-52,共4页Journal of Jiangsu Normal University：Natural Science Edition

基　　金：国家自然科学基金资助项目(61473148);江苏省自然科学基金资助项目(BK20141408)

摘　　要：基于Givens-QR分解,给出了companion矩阵的一种伪谱定义和相应的快速计算方法;利用给出的companion矩阵伪谱作为工具分析了balance技术的作用,说明了balance技术在矩阵计算中的重要性和有效性;针对多项式零点扰动,探讨了companion矩阵的结构伪谱;最后,对文中所给算法进行了数值试验与比较,说明了其正确性和有效性.Based on the Givens-QR factorization,a fast algorithm for the pseudospectra of companion matrix was proposed.The balance technique was discussed using the pseudospectra as a tool.It is shown that the balance is important and efficient in the matrix computations.Also,the structured pseudospectra of companion matrix were discussed in order to analysize the perturbation of the zeros of polynomial.Finally,numerical experiments and comparisons were presented to illustrate the correctness and the effectiveness of the proposed results.

关 键 词：伪谱 companion矩阵 BALANCE Givens-QR分解 结构伪谱 

分 类 号：O241.6[理学—计算数学]