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山东大学学报(理学版) ›› 2015, Vol. 50 ›› Issue (12): 15-22.doi: 10.6040/j.issn.1671-9352.0.2014.549

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一类区间三对角矩阵特征值的确界

蹇渊, 刘丁酉   

  1. 武汉大学数学与统计学院, 湖北 武汉 430072
  • 收稿日期:2014-12-03 修回日期:2015-03-06 出版日期:2015-12-20 发布日期:2015-12-23
  • 作者简介:蹇渊(1989-),男,硕士,研究方向为矩阵分析与应用.E-mail:yuanjian@whu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11371284)

Extremal eigenvalues of a class of tridiagonal interval matrices

JIAN Yuan, LIU Ding-you   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, Hubei, China
  • Received:2014-12-03 Revised:2015-03-06 Online:2015-12-20 Published:2015-12-23

摘要: 利用三对角矩阵特征多项式的递推式,Chebyshev多项式的性质以及特征值相关的定理来研究一类区间三对角矩阵的特征值问题, 并且获得了该类区间三对角矩阵的特征值的确界以及取得该值时所对应的矩阵。

关键词: 特征值, 三对角区间矩阵, Chebyshev多项式, 递推式

Abstract: A class of tridiagonal interval matrices is studied by the recursive characteristic polynomials and Chebyshev polynomials where some results on eigenvalues are involved. The sharp (lower and upper) bound for the eigenvalues of this class of tridiagonal interval matrices is presended, and the realization matrices whose smallest (largest) eigenvalues reach the lower(upper) bound is characterized.

Key words: recursion, eigenvalue, tridiagonal interval matrix, Chebyshev polynomial

中图分类号: 

  • O151.21
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