M-矩阵Fan积的最小特征值下界的新估计
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摘要
利用Cauchy-Schwitz不等式给出非奇异M-矩阵A和B的Fan积A★B的最小特征值下界的新估计式,并与其他文献中的估计式进行比较.数值算例表明,新估计式在一定条件下改进了Johnson和Horn给出的经典估计式,同时也优于其他已有的几个估计式,比现有的估计式更接近真值.
A new lower bound on the minimum eigenvalue for the Fan product A★Bof two nonsingular M-matrices Aand Bwas given by using Cauchy-Schwitz inequality and compared the new bound with the classical results in the literature.Numerical example showed that the new estimating formula improve the result of Johnson and Horn effectively in some cases,and also was better than the other existing results,which approached the real value than existing ones.
A new lower bound on the minimum eigenvalue for the Fan product A★Bof two nonsingular M-matrices Aand Bwas given by using Cauchy-Schwitz inequality and compared the new bound with the classical results in the literature.Numerical example showed that the new estimating formula improve the result of Johnson and Horn effectively in some cases,and also was better than the other existing results,which approached the real value than existing ones.
引文
[1]HORN R A,JOHNSON C R.Topics in matrix analysis[M].New York:Cambridge University Press,1991.
[2]FANG M Z.Bounds on eigenvalues of the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2007,425(1):7-15.
[3]HUANG R.Some inequalities for the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2008,428(7):1551-1559.
[4]LIU Q B,CHEN G L.On two inqualities for the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2009,431(5/6/7):974-984.
[5]LI Y T,LI Y Y,WANG R W,et al.Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2010,432(2/3):536-545.
[6]李艳艳,李耀堂.矩阵Hadamard积和Fan积的特征值界的估计[J].云南大学学报(自然科学版),2010,32(2):125-129.
[7]周平,李耀堂.M-矩阵及非负矩阵Hadamard积和Fan积的特征值界的估计[J].云南大学学报(自然科学版),2012,34(1):9-14.
[8]李华.矩阵Hadamard积和Fan积特征值界的新估计式[J].河南科学,2012,30(6):680-683.
[9]LIU Q B,CHEN G L,ZHAO L L.Some new bounds on the spectral radius of matrices[J].Linear Algebra Appl,2010,432(4):936-948.
[10]杜琨.矩阵Hadamard积和Fan积特征值的界[J].华东师范大学学报(自然科学版),2008(5):45-50.
[11]朱雪芳.矩阵Fan积特征值的界[J].数学的实践与认识,2012,42(2):209-213.
[12]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2003.
[13]陈景良,陈向辉.特殊矩阵[M].北京:清华大学出版社,2000.
[14]HORN R A,JOHNSON C R.Matrix analysis[M].New York:Cambridge University Press,1985.
[15]BERMAN A,PLEMMONS R J.Nonnegative matrices in the mathematical sciences[M].New York:Academic Press,1979.
[2]FANG M Z.Bounds on eigenvalues of the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2007,425(1):7-15.
[3]HUANG R.Some inequalities for the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2008,428(7):1551-1559.
[4]LIU Q B,CHEN G L.On two inqualities for the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2009,431(5/6/7):974-984.
[5]LI Y T,LI Y Y,WANG R W,et al.Some new bounds on eigenvalues of the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2010,432(2/3):536-545.
[6]李艳艳,李耀堂.矩阵Hadamard积和Fan积的特征值界的估计[J].云南大学学报(自然科学版),2010,32(2):125-129.
[7]周平,李耀堂.M-矩阵及非负矩阵Hadamard积和Fan积的特征值界的估计[J].云南大学学报(自然科学版),2012,34(1):9-14.
[8]李华.矩阵Hadamard积和Fan积特征值界的新估计式[J].河南科学,2012,30(6):680-683.
[9]LIU Q B,CHEN G L,ZHAO L L.Some new bounds on the spectral radius of matrices[J].Linear Algebra Appl,2010,432(4):936-948.
[10]杜琨.矩阵Hadamard积和Fan积特征值的界[J].华东师范大学学报(自然科学版),2008(5):45-50.
[11]朱雪芳.矩阵Fan积特征值的界[J].数学的实践与认识,2012,42(2):209-213.
[12]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2003.
[13]陈景良,陈向辉.特殊矩阵[M].北京:清华大学出版社,2000.
[14]HORN R A,JOHNSON C R.Matrix analysis[M].New York:Cambridge University Press,1985.
[15]BERMAN A,PLEMMONS R J.Nonnegative matrices in the mathematical sciences[M].New York:Academic Press,1979.