Matrix Powers in Finite Precision Arithmetic
Matrix Powers in Finite Precision Arithmetic
If A is a square matrix with spectral radius less than 1 then $A^k \to 0\,{\text{as}}\,k \to \infty $, but the powers computed in finite precision arithmetic may or may not converge. We derive a sufficient condition for $fl( A^k ) \to 0\,{\text{as}}\,k \to \infty $ and a bound on …