Abstract
The general nonlinear matrix equation X + A*X -n A I is discussed (n is a positive integer). Some necessary and sufficient conditions for existence a solution are given. Two methods for iterative computing a positive definite solution are investigated. Numerical experiments to illustrate the performance of the methods are reported.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Engwerda, J., Ran, A., Rijkeboer, A.: Necessary and Sufficient Conditions for the Existence of a Positive Definite Solution of the Matrix EquationX+A * X -1 A = Q. Linear Algebra Appl. 186 (1993) 255–275
Engwerda, J.: On the Existence of a Positive Definite Solution of the Matrix Equation X+A T X -1 A = I. Linear Algebra Appl. 194 (1993) 91–108
El-Sayed, S., Ran, A.: On an Method for Solving a Class of Nonlinear Matrix Equations. SIAM J. on Matrix Analysis /to appear/
Golub, G., van Loan C.: Matrix Computations, John Hopkins, Baltimore (1989)
Guo, C., Lancaster, P.: Iterative Solution of Two Matrix Equations. Mathematics of Computation 68 (1999) 1589–1603
Ivanov, I., El-Sayed, S.: Properties of Positive Definite Solution of the Equation X+A * X -2 A = I. Linear Algebra And Appl. 279 (1998) 303–316
Kwong, M.: Some Results on Matrix Monotone Functions. Linear Algebra And Appl. 118 (1989) 129–153
Zhan, X.: Computing the Extremal positive definite solution of a Matrix Equation. SIAM J. Sci. Comput. 247 (1996) 337–345
Zhan, X., Xie, J.: On the Matrix Equation X+A T X -1 A = Q. Linear Algebra And Appl. 247 (1996) 337–345
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hassanov, V., Ivanov, I. (2001). Positive Definite Solutions of the Equation X + A*X -n A=I . In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_44
Download citation
DOI: https://doi.org/10.1007/3-540-45262-1_44
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41814-6
Online ISBN: 978-3-540-45262-1
eBook Packages: Springer Book Archive