非奇异H-矩阵的判定及其在神经网络系统中的应用
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摘要
非奇异H-矩阵在矩阵分析和数值代数的研究中具有重要作用,但判别H-矩阵是十分困难的.通过对矩阵行标作划分的方法,给出了非奇异H-矩阵新的判定条件,改进了已有结果,将其应用在神经网络系统中,并给出数值例子说明结果的有效性.
Nonsingular H- matrices play a very important role in the research of matrix analysis and numerical algebra. But it is difficult to determine whether a matrix is a nonsingular H- matrix or not. Some sufficient conditions for nonsingular H- matrices are obtained according to the partition of the row indices,which improved some related results. And its application on neural network system is given. A numerical example is given to show its effectivity.
Nonsingular H- matrices play a very important role in the research of matrix analysis and numerical algebra. But it is difficult to determine whether a matrix is a nonsingular H- matrix or not. Some sufficient conditions for nonsingular H- matrices are obtained according to the partition of the row indices,which improved some related results. And its application on neural network system is given. A numerical example is given to show its effectivity.
引文
[1]干泰彬,黄廷祝.非奇异H-矩阵的实用性充分条件[J].计算数学,2004,20(1):109-116.GAN T B,HUANG T Z.Simple sufficient conditions for nonsingular H-matrix[J].Journal of Computation Mathematics,2004,20(1):109-116.
[2]GAN T B,HUANG T Z.Simple criteria for nonsingular H-matrix[J].Linear Algebra Appl,2003,374:317-326.
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[4]朱海,王健,廖貅武,等.非奇H-矩阵的实用判别准则[J].数学的实践与认识,2014,44(7):280-285.ZHU H,WANG J,LIAO X W,et al.Criterias for nonsingular H-matrix[J].Mathematics in Practice and Theory,2014,44(7):280-285.
[5]庹清,朱砺,刘建州.一类非奇异H-矩阵判定的新条件[J].计算数学,2008,30(2):177-182.TUO Q,ZHU L,LIU J Z.A class of conditions for nonsingular H-matrix[J].Journal of Computation Mathematics,2008,30(2):177-182.
[6]王峰.广义对角占优矩阵的判定准则[J].高等学校计算数学学报,2012,34(1):23-29.WANG F.Criteria of generalized diagonal dominance matrices[J].Journal of Computation Mathematics of Universities,2012,34(1):23-29.
[7]NEUMANN M.A note generalizations of strict diagonal dominance for real matrices[J].Linear Algebra Appl,1979,26:3-14.
[8]VARGA R S.On recurring theorems on diagonal dominance[J].Linear Algebra Appl,1976,13:1-9.
[9]李耀堂,王转德.置换相似α-下(上)半强对角占优矩阵与H-矩阵的判定[J].云南大学学报:自然科学版,2001,23(2):81-83.LI Y T,WANG Z D.Permutedly similarα-lower(Upper)semi-strongly diagonally dominant matrices and criteria for Hmatrices[J].Journal of Yunnan University:Natural Sciences Edition,2001,23(2):81-83.
[10]许洁,赵微,孙玉祥.广义对角占优矩阵的实用新判定[J].云南大学学报:自然科学版,2014,36(5):637-641.XU J,ZHAO W,SUN Y X.New criteria for generalized diagonally dominant matrices[J].Journal of Yunnan University:Natural Sciences Edition,2014,36(5):637-641.
[11]LIAO X X,LIAO Y.Stability of Hopfield type neural network(Ⅱ)[J].Science in China:Series A,1997,40(8):813-816.
[2]GAN T B,HUANG T Z.Simple criteria for nonsingular H-matrix[J].Linear Algebra Appl,2003,374:317-326.
[3]黄廷祝.非奇异H-矩阵的简捷判定[J].计算数学,1993,15(3):318-327.HUANG T Z.Simple criteria for nonsingular H-matrix[J].Journal of Computation Mathematics,1993,15(3):318-327.
[4]朱海,王健,廖貅武,等.非奇H-矩阵的实用判别准则[J].数学的实践与认识,2014,44(7):280-285.ZHU H,WANG J,LIAO X W,et al.Criterias for nonsingular H-matrix[J].Mathematics in Practice and Theory,2014,44(7):280-285.
[5]庹清,朱砺,刘建州.一类非奇异H-矩阵判定的新条件[J].计算数学,2008,30(2):177-182.TUO Q,ZHU L,LIU J Z.A class of conditions for nonsingular H-matrix[J].Journal of Computation Mathematics,2008,30(2):177-182.
[6]王峰.广义对角占优矩阵的判定准则[J].高等学校计算数学学报,2012,34(1):23-29.WANG F.Criteria of generalized diagonal dominance matrices[J].Journal of Computation Mathematics of Universities,2012,34(1):23-29.
[7]NEUMANN M.A note generalizations of strict diagonal dominance for real matrices[J].Linear Algebra Appl,1979,26:3-14.
[8]VARGA R S.On recurring theorems on diagonal dominance[J].Linear Algebra Appl,1976,13:1-9.
[9]李耀堂,王转德.置换相似α-下(上)半强对角占优矩阵与H-矩阵的判定[J].云南大学学报:自然科学版,2001,23(2):81-83.LI Y T,WANG Z D.Permutedly similarα-lower(Upper)semi-strongly diagonally dominant matrices and criteria for Hmatrices[J].Journal of Yunnan University:Natural Sciences Edition,2001,23(2):81-83.
[10]许洁,赵微,孙玉祥.广义对角占优矩阵的实用新判定[J].云南大学学报:自然科学版,2014,36(5):637-641.XU J,ZHAO W,SUN Y X.New criteria for generalized diagonally dominant matrices[J].Journal of Yunnan University:Natural Sciences Edition,2014,36(5):637-641.
[11]LIAO X X,LIAO Y.Stability of Hopfield type neural network(Ⅱ)[J].Science in China:Series A,1997,40(8):813-816.