The improved disc theorems for the Schur complements of diagonally dominant matrices
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- 作者：Juan Zhang (1)
Jianzhou Liu (1) (2)
Gen Tu (2) - 关键词：Schur complement ; diagonally dominant matrices ; eigenvalue ; Gerschgorin theorem
- 刊名：Journal of Inequalities and Applications
- 出版年：2013
- 出版时间：December 2013
- 年：2013
- 卷：2013
- 期：1
- 全文大小：261KB
- 参考文献：1. Liu JZ, Huang ZJ: The Schur complements of 纬 -diagonally and product 纬 -diagonally dominant matrix and their disc separation. / Linear Algebra Appl. 2010, 432:1090鈥?104. 10.1016/j.laa.2009.10.021">CrossRef
2. Liu JZ, Huang ZJ, Zhang J: The dominant degree and disc theorem for the Schur complement. / Appl. Math. Comput. 2010, 215:4055鈥?066. 10.1016/j.amc.2009.12.063">CrossRef
3. Xiang SH, Zhang SL: A convergence analysis of block accelerated over-relaxation iterative methods for weak block H -matrices to partition 蟺 . / Linear Algebra Appl. 2006, 418:20鈥?2. 10.1016/j.laa.2006.01.013">CrossRef
4. Horn RA, Johnson CR: / Topics in Matrix Analysis. Cambridge University Press, New York; 1991. 10.1017/CBO9780511840371">CrossRef
5. Smith R: Some interlacing properties of the Schur complement of a Hermitian matrix. / Linear Algebra Appl. 1992, 177:137鈥?44. 10.1016/0024-3795(92)90321-Z">CrossRef
6. Carlson D, Markham T: Schur complements on diagonally dominant matrices. / Czechoslov. Math. J. 1979,29(104):246鈥?51.
7. Ikramov KD: Invariance of the Brauer diagonal dominance in Gaussian elimination. / Moscow. Univ. Comput. Math. Cybern. 1989, 2:91鈥?4.
8. Li B, Tsatsomeros M: Doubly diagonally dominant matrices. / Linear Algebra Appl. 1997, 261:221鈥?35. 10.1016/S0024-3795(96)00406-5">CrossRef
9. Golub GH, Van Loan CF: / Matrix Computations. 3rd edition. Johns Hopkins University Press, Baltimore; 1996.
10. Kress R: / Numerical Analysis. Springer, New York; 1998. 10.1007/978-1-4612-0599-9">CrossRef
11. Liu JZ, Li JC, Huang ZH, Kong X: Some properties on Schur complement and diagonal-Schur complement of some diagonally dominant matrices. / Linear Algebra Appl. 2008, 428:1009鈥?030. 10.1016/j.laa.2007.09.008">CrossRef
12. Liu JZ, Huang YQ: The Schur complements of generalized doubly diagonally dominant matrices. / Linear Algebra Appl. 2004, 378:231鈥?44. 10.1016/j.laa.2003.09.012">CrossRef
13. Liu JZ, Huang YQ: Some properties on Schur complements of H -matrices and diagonally dominant matrices. / Linear Algebra Appl. 2004, 389:365鈥?80. 10.1016/j.laa.2004.04.012">CrossRef
14. Liu JZ, Zhang FZ: Disc separation of the Schur complements of diagonally dominant matrices and determinantal bounds. / SIAM J. Matrix Anal. Appl. 2005, 27:665鈥?74. 10.1137/040620369">CrossRef
15. Liu JZ: Some inequalities for singular values and eigenvalues of generalized Schur complements of products of matrices. / Linear Algebra Appl. 1999, 286:209鈥?21. 10.1016/S0024-3795(98)10156-8">CrossRef
16. Liu JZ, Zhu L: A minimum principle and estimates of the eigenvalues for Schur complements of positive semidefinite Hermitian matrices. / Linear Algebra Appl. 1997, 265:123鈥?45. 10.1016/S0024-3795(96)00595-2">CrossRef
17. Liu JZ, Zhang J, Liu Y: The Schur complement of strictly doubly diagonally dominant matrices and its application. / Linear Algebra Appl. 2012, 437:168鈥?83. 10.1016/j.laa.2012.02.001">CrossRef - 作者单位：Juan Zhang (1)
Jianzhou Liu (1) (2)
Gen Tu (2)
1. Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China
2. Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education, Xiangtan University, Xiangtan, Hunan, 411105, P.R. China - ISSN：1029-242X
文摘
The theory of Schur complement is very important in many fields such as control theory and computational mathematics. In this paper, applying the properties of Schur complement, utilizing some inequality techniques, some new estimates of diagonally dominant degree on the Schur complement of matrices are obtained, which improve some relative results. Further, as an application of these derived results, we present some distributions for the eigenvalues of the Schur complements. Finally, the numerical example is given to show the advantages of our derived results. MSC: 15A45, 15A48.