Abstract
The paper deals with the derivation of improved perturbation bounds for the matrix expression and their application to the sensitivity analysis and the solution of fractional–affine matrix equations. An estimate of the overall error in the solution of matrix equations is also given.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Grebenikov, E., Ryabov, Y.: Constructive Methods for Analysis of Nonlinear Systems. Nauka, Moscow (1979) (in Russian)
Higham, N., Konstantinov, M., Mehrmann, V., Petkov, P.: The Sensitivity of Computational Control Problems. IEEE Control Syst. Magazine 24, 28–43 (2004)
Konstantinov, M., Gu, D., Mehrmann, V., Petkov, P.: Perturbation Theory for Matrix Equations. Elsevier, Amsterdam (2003)
Konstantinov, M., Petkov, P.: Note on Perturbation theory for algebaic Riccati equations (SIAM J. Matrix Anal. Appl. 19, 39–65, by J.G. Sun (1998)). SIAM J. Matrix Anal. Appl. 21, 327 (1999)
Konstantinov, M., Petkov, P., Gu, D.: Improved Perturbation Bounds for General Quadratic Matrix Equations. Numer. Funct. Anal. Opim. 20, 717–736 (1999)
Konstantinov, M., Stanislavova, M., Petkov, P.: Perturbation Bounds and Characterisation of the Solution of the Associated Algebraic Riccati Equation. Linear Algebra Appl. 285, 7–31 (1998)
Lika, D., Ryabov, Y.: Iterative Methods and Lyapunov Majorant Equations in Non–Linear Osillation Theory. Shtiinca, Kishinev (in Russian) (1974)
Petkov, P., Christov, N., Konstantinov, M.: Computational Methods for Linear Control Problems. Prentice Hall, Hemel Hempstead (1991)
Stewart, S., Sun, J.: Matrix Perturbation Theory. Academic Press, New York (1990)
Sun, J.: Perturbation Theory for Algebraic Riccati Equations. SIAM J. Matrix Anal. Appl. 19, 39–65 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Konstantinov, M.M., Petkov, P.H., Christov, N.D. (2009). Perturbation Bounds for Certain Matrix Expressions and Numerical Solution of Matrix Equations. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_7
Download citation
DOI: https://doi.org/10.1007/978-3-642-00464-3_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00463-6
Online ISBN: 978-3-642-00464-3
eBook Packages: Computer ScienceComputer Science (R0)