M-矩阵Fan积的特征值的新下界
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摘要
特征值界的估计是矩阵论中重要的研究课题。文中借助Brauer定理与Gerschgorin定理得到非奇异M-矩阵A和B的Fan积的特征值下界新的估计结果。数值算例表明新的下界在某些特定条件下优于Johnson和Horn所给结果,并且也优于其它文献中有关的结论。
The estimation of the bounds on the eigenvalue is an important research topic in the matrices theories.In this paper,the new estimators of the lower bounds on the eigenvalue for the Fan product of nonsingular M-matrices and were obtained by using Brauer theorem and Gerschgorin theorem. Numerical example shows that the new lower bounds are superior to the result given by Johnson and Horn under certain conditions,and are also superior to other related conclusions in the literature.
The estimation of the bounds on the eigenvalue is an important research topic in the matrices theories.In this paper,the new estimators of the lower bounds on the eigenvalue for the Fan product of nonsingular M-matrices and were obtained by using Brauer theorem and Gerschgorin theorem. Numerical example shows that the new lower bounds are superior to the result given by Johnson and Horn under certain conditions,and are also superior to other related conclusions in the literature.
引文
[1]陈景良,陈向辉.特殊矩阵[M].北京:清华大学出版社,2000.
[2]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2003.
[3]HORN R A,JOHNSON C R.Topics in Matrix Analysis[M].New York:Cambridge University Press,1991.
[4]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.
[5]HUANG R.Some inequalities for the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2008,428(7):1551-1559.
[6]LI Y T,LI Y Y,WANG R W,et al.Some new bounds on eigenvalue of the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2010,432(2/3):536-545.
[7]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(S5/7):974-984.
[8]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.
[9]GUO Q P,LI H B,LENG J S.New inequalities on eigenvalues of the Hadamardproduct and the Fan product of matrices[J].J Inequal Appl,2013,2013:1-11.
[10]VARGA R S.Minimal Gerschgorin sets[J].Pacific J Math,1965,15(2):719-729.
[11]HORN R A,JOHNSON C R.Matrix Analysis[M].New York:Cambridge University Press,1985.
[12]BERMAN A,PLEMMONS R J.Nonnegative Matrices in the Mathematical Sciences[M].New York:Academic Press,1979.
[2]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2003.
[3]HORN R A,JOHNSON C R.Topics in Matrix Analysis[M].New York:Cambridge University Press,1991.
[4]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.
[5]HUANG R.Some inequalities for the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2008,428(7):1551-1559.
[6]LI Y T,LI Y Y,WANG R W,et al.Some new bounds on eigenvalue of the Hadamard product and the Fan product of matrices[J].Linear Algebra Appl,2010,432(2/3):536-545.
[7]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(S5/7):974-984.
[8]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.
[9]GUO Q P,LI H B,LENG J S.New inequalities on eigenvalues of the Hadamardproduct and the Fan product of matrices[J].J Inequal Appl,2013,2013:1-11.
[10]VARGA R S.Minimal Gerschgorin sets[J].Pacific J Math,1965,15(2):719-729.
[11]HORN R A,JOHNSON C R.Matrix Analysis[M].New York:Cambridge University Press,1985.
[12]BERMAN A,PLEMMONS R J.Nonnegative Matrices in the Mathematical Sciences[M].New York:Academic Press,1979.