Matrix Powers in Finite Precision Arithmetic

@article{Higham1995MatrixPI,
  title={Matrix Powers in Finite Precision Arithmetic},
  author={Nicholas J. Higham and Philip A. Knight},
  journal={SIAM J. Matrix Analysis Applications},
  year={1995},
  volume={16},
  pages={343-358}
}
If A is a square matrix with spectral radius less than 1 then A k 0 as k c, but the powers computed in finite precision arithmetic may or may not converge. We derive a sufficient condition for fl(Ak) 0 as k x) and a bound on [[fl(Ak)[[, both expressed in terms of the Jordan canonical form of A. Examples show that the results can be sharp. We show that the… CONTINUE READING