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非负矩阵最大特征值的新界值

殷剑宏   

  1. 合肥工业大学计算机科学与信息学院 合肥 230009
  • 出版日期:2002-04-20 发布日期:2002-04-20

殷剑宏. 非负矩阵最大特征值的新界值[J]. 数值计算与计算机应用, 2002, 23(4): 292-295.

NEW BOUNDS FOR THE GREATEST CHARACTERISTIC ROOT OF A NONNEGATIVE MATRIX

  1. Yin Jianhong(Department of Computer Science and Technology, Hefei University of Technology, Hefei 230009 )
  • Online:2002-04-20 Published:2002-04-20
§ 非负矩阵理论作为一种基本工具,被广泛地应用于数值分析、图论、计算机科学、管理科学等领域中.对非负矩阵最大特征值进行估计,又是该理论的核心问题之一.如果上下界能表示为矩阵元素的易于计算的函数,那么这种估计的价值更高.最著名且用得最多的当算G.Frobenius[1]界值. Frobenius界值定理.设r是n阶非负矩阵A的最大特征值,ri(i=1,2,…,n)为A的i行行和,则 minri≤r≤maxri(1.1) i i   对于A的i列列和Ci(i=1,2,…,n),有相同的结论. 对于有非零行和的非负矩阵A,H.Minc[2]把(1.1)式改进为(1.2)
Computing the bounds for the greatest characteristic root of a nonnegative matrix, is important part in the theory of nonnegative matrices. It is more practical value when their bounds are expressed easily calculated function in element of matrix. In this paper, we obtain new bounds for the greatest eigenvalue of a nonnegative matrix. Compared with the results of Frobenius, the new bounds are sharper.
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[1] G.Probenius,Uber Matrizen aUS nichtnegativen Elementen,Sitzungsber.Kon.ass.Akad.wiss.Berlin,(1912) ,465-477.
[2] H.Minc,Nonnegative Matrices,Wiley,New York,1988,11-19,24-36.
[3] W.Ledermann,Bounds for the greatest latent root of a positive matrix,J.London Math.Soc.25(1950) ,265-268.
[4] A.Ostrowski,Bounds for the greatest latent root of a positive matrix,J.London Math.Soc.27(1952) ,253-256.
[5] A.Brauer,The theorems of Ledermann and Ostrowski on positive matrices,Duke Math.J.24(1957) ,265-274.
[6] Shu-Lin Liu,Bounds for the Greatest Characteristic Root of a Nonnegative Matrix,LINEARALGEBRA AND ITS APPLICATIONs 239(1996) .151-160.
[7] Abraham Berman,Robert J.Plemmons,Nonnegative Matrices in the Mathematical Sciences,Society for Industrial and Applied Mathematics(SIAM),1994.
[8] H.威尔金森著,石钟慈、邓健新译,代数特征值问题,科学出版社, 1987.
[9] H.MINC著,杨尚骏、卢业广、杜古佩译编,非负矩阵,辽宁教育出版社, 1991年.
[10] 殷剑宏,求非负矩阵最大特征值与特征向量的C-W方法,合肥工业大学学报(自然科学版),23:5(2000) ,752-756.
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