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2015 | 13 | 1 |
Tytuł artykułu

The estimates of diagonally dominant degree and eigenvalues inclusion regions for the Schur complement of block diagonally dominant matrices

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The theory of Schur complement plays an important role in many fields, such as matrix theory and control theory. In this paper, applying the properties of Schur complement, some new estimates of diagonally dominant degree on the Schur complement of I(II)-block strictly diagonally dominant matrices and I(II)-block strictly doubly diagonally dominant matrices are obtained, which improve some relative results in Liu [Linear Algebra Appl. 435(2011) 3085-3100]. As an application, we present several new eigenvalue inclusion regions for the Schur complement of matrices. Finally, we give a numerical example to illustrate the advantages of our derived results.
Wydawca
Czasopismo
Rocznik
Tom
13
Numer
1
Opis fizyczny
Daty
otrzymano
2015-05-08
zaakceptowano
2015-10-14
online
2015-11-05
Twórcy
autor
  • College of Science, Guizhou Minzu University, Guiyang, Guizhou 550025, P.R. China
autor
  • College of Science, Guizhou Minzu University, Guiyang, Guizhou 550025, P.R. China
Bibliografia
  • [1] Cvetkovi K c, Lj: A new subclass of H-matrices. Appl. Math. Comput. 208(2009), 206-210.[WoS]
  • [2] Ikramov, K.D.: Invariance of the Brauer diagonal dominance in gaussian elimination. Moscow University Comput. Math. Cybernet..N2/ (1989),91-94.
  • [3] Li, B., Tsatsomeros, M.: Doubly diagonally dominant matrices. Linear Algebra Appl. 261(1997), 221-235.
  • [4] Liu, J.Z., Huang, Z.H., Zhu, L., Huang, Z.J.: Theorems on Schur complements of block diagonally dominant matrices and theirapplication in reducing the order for the solution of large scale linear systems. Linear Algebra Appl. 435(2011), 3085-3100.[WoS]
  • [5] Liu, J.Z., Li, J.C., Huang, Z.H., Kong, X.: Some propertes on Schur complement and diagonal Schur complement of somediagonally dominant matrices. Linear Algebra Appl. 428(2008), 1009-1030.
  • [6] Liu, J.Z., Huang, Z.J.: The Schur complements of -diagonally and product -diagonally dominant matrix and their discseparation. Linear Algebra Appl. 432(2010), 1090-1104.[WoS]
  • [7] Liu, J.Z., Huang, Z.J.: The dominant degree and disc theorem for the Schur complement. Appl. Math. Comput. 215(2010),4055-4066.[WoS]
  • [8] Liu, J.Z., Zhang, F.Z.: Disc separation of the Schur complements of diagonally dominant matrices and determinantal bounds.SIAM J. Matrix Anal. Appl. 27(2005) 665-674.
  • [9] Liu, J.Z., Huang, Y.Q.: The Schur complements of generalized doubly diagonally dominant matrices. Linear Algebra Appl.378(2004), 231-244.
  • [10] Li, Y.T., Ouyang, S.P., Cao, S.J., Wang, R.W.: On diagonal-Schur complements of block diagonally dominant matrices. Appl.Math. Comput. 216(2010), 1383-1392.[WoS]
  • [11] Zhang, C.Y., Li, Y.T., Chen, F.: On Schur complement of block diagonally dominant matrices. Linear Algebra Appl. 414(2006),533-546.
  • [12] Zhang, F.Z.: The Schur complement and its applications. Springer Press, New York, 2005.
  • [13] Demmel, J.W.: Applied numerical linear algebra. SIAM Press, Philadelphia, 1997.
  • [14] Golub, G.H., Van Loan, C.F.: Matrix computationss. third ed., Johns Hopkins University Press, Baltimore, 1996.
  • [15] Kress, R.: Numerical Analysis. Springer Press, New York, 1998.
  • [16] Xiang, S.H., Zhang, S.L.: A convergence analysis of block accelerated over-relaxation iterative methods for weak blockH-matrices to partion π. Linear Algebra Appl. 418(2006), 20-32.
  • [17] Berman, A., Plemmons, R.J.: Nonnegative matrices in the mathematical sciences. SIAM Press, Philadelphia, 1994, pp. 185.
  • [18] Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, New York, 1991, pp. 117.
  • [19] Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, New York, 1985, pp. 301.
  • [20] Salas, N.: Gershgorin’s theorem for matrices of operators. Linear Algebra Appl. 291(1999), 15-36.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2015-0072
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