严格对角占优矩阵与Nekrasov矩阵的子直和
Subdirect Sums of Strictly Diagonally Dominant Matrices and Nekrasov Matrices

作者: 赵晶 , 胡汭炎 , 李耀堂 :云南大学数学与统计学院,云南 昆明;

关键词: Nekrasov矩阵严格对角占优子直和Nekrasov Matrix Strictly Diagonally Dominant Subdirect Sum

摘要: 给出了严格对角占优矩阵与Nekrasov矩阵的子直和为Nekrasov矩阵的充分条件,并用数值例子对所给结论进行了说明。

Abstract: A sufficient condition ensuring that the subdirect sum of strictly diagonally dominant matrix and Nekrasov matrix is in the class of Nekrasov matrices is given. And the conclusion is illustrated by a numerical example.

文章引用: 赵晶 , 胡汭炎 , 李耀堂 (2016) 严格对角占优矩阵与Nekrasov矩阵的子直和。 应用数学进展, 5, 505-515. doi: 10.12677/AAM.2016.53061

参考文献

[1] Fallat, S.M. and Johnson, C.R. (1999) Sub-Direct Sums and Positivity Classes of Matrices. Linear Algebra and its Applications, 288, 149-173.
http://dx.doi.org/10.1016/S0024-3795(98)10194-5

[2] Bru, R., Pedroche, F. and Szyld, D.B. (2005) Subdirect Sums of Nonsingular M-Matrices and of Their Inverse. Electronic Journal of Linear Algebra, 13, 162-174.

[3] Frommer, A. and Szyld, D.B. (1999) Weighted Max Norms, Splittings, and Overlapping Additive Schwarz Iterations. Numerische Mathematik, 83, 259-278.
http://dx.doi.org/10.1007/s002110050449

[4] Bru, R., Pedroche, F. and Szyld, D.B. (2005) Additive Schwarz Iterations for Markov Chains. SIAM Journal on Matrix Analysis and Applications, 27, 445-458.
http://dx.doi.org/10.1137/040616541

[5] Bru, R., Pedroche, F. and Szyld, D.B. (2006) Subdirect Sums of S-Strictly Diagonally Dominant Matrices. The Electronic Journal of Linear Algebra, 15, 201-209.

[6] Zhu, Y. and Huang, T.Z. (2007) Subdirect Sum of Doubly Diagonally Dominant Matrices. The Electronic Journal of Linear Algebra, 16, 171-182.

[7] Bru, R., Cvetkovic, L., Kostic, V. and Pedroche, F. (2010) Sums of Strictly Diagonally Dominant Matrices. Linear and Multilinear Algebra, 58, 75-78.
http://dx.doi.org/10.1080/03081080802379725

[8] Li, C.Q., Liu, Q.L., Gao, L. and Li, Y.T. (2016) Subdirect Sums of Nekrasov Matrices. Linear Multilinear Algebra, 64, 208-218.
http://dx.doi.org/10.1080/03081087.2015.1032198

[9] Cvetkovic, L. (2006) H-Matrix Theory vs. Eigenvalue Location. Numerical Algorithms, 42, 229-245.
http://dx.doi.org/10.1007/s11075-006-9029-3

[10] Horn, R.A. and Johnson, C.R. (1985) Matrix Analysis. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511810817

[11] Berman, A. and Plemmons, R.J. (1979) Nonnegative Matrices in the Ma-thematical Sciences. Academic Press, New York.

[12] Li, W. (1998) On Nekrasov Matrices. Linear Algebra and its Applications, 281, 87-96.
http://dx.doi.org/10.1016/S0024-3795(98)10031-9

[13] Cvetkovic, L., Dai, P.F., Doroslovackic, K. and Li, Y.T. (2013) Infinity Norm Bounds for the Inverse of Nekrasov Matrices. Applied Mathematics and Computation, 219, 5020-5024.
http://dx.doi.org/10.1016/j.amc.2012.11.056

分享
Top