How to solve the matrix equation XA-AX=f(X)

@article{Bourgeois2010HowTS,
title={How to solve the matrix equation XA-AX=f(X)},
author={G. Bourgeois},
journal={arXiv: Rings and Algebras},
year={2010}
}
• G. Bourgeois
• Published 2010
• Mathematics
• arXiv: Rings and Algebras
Let f be an analytic function defined on a complex domain Omega and A be a (n,n) complex matrix. We assume that there exists a unique alpha satisfying f(alpha)=0. When f'(alpha)=0 and A is non derogatory, we solve completely the equation XA-AX=f(X). This generalizes Burde's results. When f'(alpha) is not zero, we give a method to solve completely the equation XA-AX=f(X): we reduce the problem to solve a sequence of Sylvester equations. Solutions of the equation f(XA-AX)=X are also given in… Expand
15 Citations

References

SHOWING 1-10 OF 13 REFERENCES
On the Matrix Equation Xa − Ax = X
• P Dietrich Burde
• 2004
• 6
• Highly Influential
Functions of matrices - theory and computation
• 1,609
• Highly Influential
• PDF
Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches
• Mathematics, Computer Science
• SIAM J. Matrix Anal. Appl.
• 2001
• 108
• PDF
The Riccati equation
• Mathematics
• 1991
• 360
Algebraic Riccati equations
• Mathematics, Computer Science
• 1995
• 1,318
• PDF