Department of Mathematical Sciences, National Chengchi University, Taipei, Taiwan, Republic of China ; Department of Mathematics, Naval Postgraduate School, Monterey, California 93943
Abstract:
In applying the 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 iteration. Experimental testing demonstrates that the unimodular shift produces more efficient numerical convergence.