非負矩陣Hadam ard積和M-矩陣Fan積的特征值界的估計

周平,李耀堂

(1.文山學院數理系,云南 文山 663000;2.云南大學數學與統計學院,云南 昆明 650091)

非負矩陣Hadam ard積和M-矩陣Fan積的特征值界的估計

周平1,李耀堂2

(1.文山學院數理系,云南 文山 663000;2.云南大學數學與統計學院,云南 昆明 650091)

矩陣的Hadamard積和Fan積是矩陣理論研究的重要問題之一.對于兩個非負矩陣A和B的Hadamard積,給出了它的譜半徑上界的兩個新的估計式;同時對于兩個非奇異M-矩陣A和B的Fan積,給出了它的最小特征值下界的兩個新的估計式;算例表明,所得估計式在某些情況下比現有估計式更為精確,并且這些估計式都只依賴于矩陣A和B的元素,更容易計算.

非負矩陣;M-矩陣;Hadamard積;Fan積;譜半徑;最小特征值

1 預備知識

2 兩個非負矩陣的H adam ard積的譜半徑的上界

3 q(A?B)的下界

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Estimating of bounds on eigenvalues of the H adam ard p roduct for nonnegative m atrices and the Fan p roduct of M-m atrices

Zhou Ping1,Li Yaotang2

(1.School of M athem atics and Physics,Wenshan University,Wenshan 663000,China; 2.School of M athem atics and Statistics,Yunnan University,Kunm ing 650091,China)

The Hadamard p roduct and the Fan product ofmatrices are im portant prob lem s in thematrices theories.For the Hadam ard product of two nonnegative m atrices A and B,two new upper bounds of the spectral radius are given.For the Fan p roduct of two M-m atrices A and B,two new lower bounds of the smallest eigenvalues are given.The given numerical exam p les show that these estimating formulas im prove several existing resu lts in som e cases,and these bounds are easier to calcu late for they are on ly depending on the entries ofm atrices A and B.

nonnegativematrix,M-matrix,Hadamard product,Fan p roduct,spectral radius, sm allest eigenvalue

O151.21

A

1008-5513(2012)06-0826-08

2011-12-03.

國家自然科學基金(10961027).

周平(1987-),碩士,助教,研究方向:矩陣理論及其應用研究.

李耀堂(1958-),博士,教授,研究方向:數值計算及其應用研究.

2010 M SC:15A 42,15A 69