广义严格对角占优矩阵的一种判别法
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摘要
广义严格对角占优矩阵是一类很重要的特殊矩阵,在理论与实际中具有广泛的应用,有关它的判别一直是人们研究的重点.本文给出广义严格对角占优矩阵的一种迭代判别法,证明了相应的收敛性理论,并用数值算例展示了该判别法的有效性.
Generalized strictly diagonally dominant matrix is a kind of special matrix which has many applications in theory and practice, and research on its discrimination has become a hot topic in recent years. In this paper, an iterative method is proposed for identifying a matrix to be a generalized strictly diagonally dominant matrix or not. Theoretical analysis and numerical examples are given to show that the method is effective and efficient.
Generalized strictly diagonally dominant matrix is a kind of special matrix which has many applications in theory and practice, and research on its discrimination has become a hot topic in recent years. In this paper, an iterative method is proposed for identifying a matrix to be a generalized strictly diagonally dominant matrix or not. Theoretical analysis and numerical examples are given to show that the method is effective and efficient.
引文
[1]ALANELLI M,HADJIDIMOS A.A new iterative criterion for H-matrices[J].SIAM J.Matrix Appl.,2006,29:160-176.
[2]BERMAN A,PLEMMONS R J.Nonnegative Matrices in the Mathematical Sciences[M].New York:Academic Press,1994.
[3]DAILEY M,DOPICO F,YE Q.A new perturbation bound for the LDU factorization of diagonally dominant matrices[J].SIAM J.Matrix Anal.Appl.,2014,35(3):904-930.
[4]范迎松,陆全,徐仲,高慧敏.非奇异H-矩阵的一组细分迭代判别准则[J].工程数学学报,2012,31(6):877-882.
[5]高慧敏,陆全,徐仲,山瑞平.非奇H-矩阵的一组含参数迭代判定准则[J].高校应用数学学报,2012,27(4):439-448.
[6]高慧敏,陆全,徐仲,山瑞平.非奇H-矩阵的一组细分迭代判定条件[J].工程数学学报,2014,33(6):329-337.
[7]GUAN J R,LU L Z,LI R C,SHAO R X.Self-Corrective iterations for generalized diagonally dominant matrices[J].J.Comput.Appl.Math.,2016,302:285-300.
[8]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2007.
[9]黄政阁,徐仲,陆全,崔静静.非奇H-矩阵的一组新的判定条件[J].高等学校计算数学学报,2016,38(4):330-342.
[10]KOHNO T,NIKI H,SAWAMI H,GAO Y M.An iterative test for H-matrix[J].J.Comput.Appl.Math.,2000,115:349-355.
[11]KOEV P,DOPICO F.Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices[J].Numer.Math.,2011,119:337-371.
[12]LI H B,HUANG T Z.On a new criterion for the H-matrix property[J].Applied Mathematics Letters.,2006,19:1134-1142.
[13]OJIRO K,NIKI H,USUI M.A new criterion for H-matrices[J].J.Comput.Appl.Math.,2003,150:293-302.
[14]SPIELMAN D A,TENG S H.Nearly-linear time algorithms for preconditioning and solving symmetric,diagonally dominant linear systems[J].SIAM J.Matrix Anal.Appl.,2014,35(3):835-885.
[15]徐仲,陆全,张凯院等.H-矩阵类的理论及应用[M].北京:科学出版社,2013.
[16]VARGA R S.Matrix Iterative Analysis[M].Berlin:Springer-Verlag,2000.
[2]BERMAN A,PLEMMONS R J.Nonnegative Matrices in the Mathematical Sciences[M].New York:Academic Press,1994.
[3]DAILEY M,DOPICO F,YE Q.A new perturbation bound for the LDU factorization of diagonally dominant matrices[J].SIAM J.Matrix Anal.Appl.,2014,35(3):904-930.
[4]范迎松,陆全,徐仲,高慧敏.非奇异H-矩阵的一组细分迭代判别准则[J].工程数学学报,2012,31(6):877-882.
[5]高慧敏,陆全,徐仲,山瑞平.非奇H-矩阵的一组含参数迭代判定准则[J].高校应用数学学报,2012,27(4):439-448.
[6]高慧敏,陆全,徐仲,山瑞平.非奇H-矩阵的一组细分迭代判定条件[J].工程数学学报,2014,33(6):329-337.
[7]GUAN J R,LU L Z,LI R C,SHAO R X.Self-Corrective iterations for generalized diagonally dominant matrices[J].J.Comput.Appl.Math.,2016,302:285-300.
[8]黄廷祝,杨传胜.特殊矩阵分析及应用[M].北京:科学出版社,2007.
[9]黄政阁,徐仲,陆全,崔静静.非奇H-矩阵的一组新的判定条件[J].高等学校计算数学学报,2016,38(4):330-342.
[10]KOHNO T,NIKI H,SAWAMI H,GAO Y M.An iterative test for H-matrix[J].J.Comput.Appl.Math.,2000,115:349-355.
[11]KOEV P,DOPICO F.Perturbation theory for the LDU factorization and accurate computations for diagonally dominant matrices[J].Numer.Math.,2011,119:337-371.
[12]LI H B,HUANG T Z.On a new criterion for the H-matrix property[J].Applied Mathematics Letters.,2006,19:1134-1142.
[13]OJIRO K,NIKI H,USUI M.A new criterion for H-matrices[J].J.Comput.Appl.Math.,2003,150:293-302.
[14]SPIELMAN D A,TENG S H.Nearly-linear time algorithms for preconditioning and solving symmetric,diagonally dominant linear systems[J].SIAM J.Matrix Anal.Appl.,2014,35(3):835-885.
[15]徐仲,陆全,张凯院等.H-矩阵类的理论及应用[M].北京:科学出版社,2013.
[16]VARGA R S.Matrix Iterative Analysis[M].Berlin:Springer-Verlag,2000.