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
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References

SHOWING 1-10 OF 13 REFERENCES
On the Matrix Equation Xa − Ax = X
  • P Dietrich Burde
  • 2004
  • 6
  • Highly Influential
On the matrix equation XA-AX=X^p
  • 19
  • PDF
Functions of matrices - theory and computation
  • 1,609
  • Highly Influential
  • PDF
Solving a Quadratic Matrix Equation by Newton's Method with Exact Line Searches
  • N. Higham, H. Kim
  • Mathematics, Computer Science
  • SIAM J. Matrix Anal. Appl.
  • 2001
  • 108
  • PDF
The Riccati equation
  • 360
Algebraic Riccati equations
  • 1,318
  • PDF
...
1
2
...