Convergence of the unitary ππ algorithm with a unimodular Wilkinson shift
Tai-Lin Wang, William B. Gragg Β· Mathematics of Computation Β· 2002
In applying the Q R Q\!R algorithm to compute the eigenvalues of a unitary Hessenberg matrix, a projected Wilkinson shift of unit modulus is proposed and proved to give global convergence with (at least) a quadratic asymptotic rate for the Q R Q\!R iteration. Experimental testing demonstrates that the unimodular shift produces more efficient numerical convergence.