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New Perturbation Bounds Analysis of a Kind of Generalized Saddle Point Systems

Part of: Numerical linear algebra

Published online by Cambridge University Press:  31 January 2017

Wei-Wei Xu ,
Mao-Mao Liu ,
Lei Zhu  and
Hong-Fu Zuo
Wei-Wei Xu*
Affiliation:
College of Science, Hohai University, Nanjing 210098, P.R. China
Mao-Mao Liu
Affiliation:
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P.R. China
Lei Zhu
Affiliation:
College of Engineering, Nanjing Agricultural University, Nanjing 210031, P.R. China
Hong-Fu Zuo
Affiliation:
College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R. China
*
*Corresponding author. Email address:wwx19840904@sina.com (W.-W. Xu)
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Abstract

In this paper we consider new perturbation bounds analysis of a kind of generalized saddle point systems. We provide perturbation upper bounds for the solutions of generalized saddle point systems, which extend the corresponding results in [W.-W. Xu, W. Li, New perturbation analysis for generalized saddle point systems, Calcolo., 46(2009), pp. 25-36] to more general cases.

Keywords

Generalized saddle point systemperturbation bounds analysis

MSC classification

Secondary: 65F35: Matrix norms, conditioning, scaling

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 1 , February 2017 , pp. 116 - 124
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Xu, W.-W., Li, W., New perturbation analysis for generalized saddle point systems, Calcolo, 46(2009), pp. 25–36.CrossRefGoogle Scholar
[2] Xu, W.-W., Li, W. and Jin, X.-Q., Backward error analysis for eigenproblems involving conjugate symplectic matrices, East Asian Journal on Applied Mathematics, 4(2015), pp. 312–326.Google Scholar
[3] Xu, W.-W., On eigenvalue bounds of two classes of two-by-two block indefinite matrices, Applied Mathematics and Computation, 219(2013), pp. 6669–6679.Google Scholar
[4] Zhu, L., Xu, W.-W. and Yang, X.-D., Perturbation bounds and condition numbers for a complex indefinite linear algebraic system, East Asian Journal on Applied Mathematics, 2(2016), pp. 211–221.Google Scholar
[5] Benzi, M., Golub, G.H., Liesen, J., Numerical solutions for saddle point problems, Acta Numerica, 14(2005), pp. 1–137.Google Scholar
[6] Botchev, M.A., Golub, G.H., A class of nonsymmetric preconditioners for saddle point problems, SIAM Journal on Matrix Analysis and Applications, 27(4)(2006), pp. 1125–1149.Google Scholar
[7] Lin, Y.-Q., Wei, Y.-M., Corrected Uzawa methods for solving large nonsymmetric saddle point problems, Applied Mathematics and Computation, 183(2006), pp. 1108–1120.Google Scholar
[8] Peng, X.-F., Li, W., Xiang, S.-H., New preconditioners based on symmetric-triangular decomposition for saddle point problems, Computing, 93(2011), pp. 27–46.Google Scholar
[9] Bai, Z.-Z., Structured preconditioners for nonsingular matrices of block two-by-two structures, Mathematics of Computation, 75:254(2006), pp. 791–815.CrossRefGoogle Scholar
[10] Bai, Z.-Z., Golub, G.H., Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems, IMA Journal of Numerical Analysis, 27:1(2007), pp. 1–23.Google Scholar
[11] Bai, Z.-Z., Wang, Z.-Q., On parameterized inexact Uzawa methods for generalized saddle point problems, Linear Algebra and its Applications, 428:11-12(2008), pp. 2900–2932.Google Scholar
[12] Bai, Z.-Z., Golub, G.H., Pan, J.-Y., Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems, Numerische Mathematik, 98(2004), pp. 1–32.Google Scholar
[13] Bai, Z.-Z., Parlett, B.N., Wang, Z.-Q., On generalized successive overrelaxation methods for augmented linear systems, Numerische Mathematik, 102(2005), pp. 1–38.Google Scholar
[14] Bai, Z.-Z., Optimal parameters in the HSS-like methods for saddle-point problems, Numerical Linear Algebra with Applications, 16(2009), pp. 447–479.Google Scholar
[15] Bai, Z.-Z., Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks, Journal of Computational and Applied Mathematics, 237(2013), pp. 295–306.Google Scholar