Linear convergence in the shifted $QR$ algorithm

Steve Batterson, David Day
1992 Mathematics of Computation  
Global and asymptotic convergence properties for the QR algorithm with Francis double shift are established for certain orthogonal similarity classes of 4 x 4 real matrices. It is shown that in each of the classes every unreduced Hessenberg matrix will decouple and that the rate of decoupling is almost always linear. The effect of the EISPACK exceptional shift strategy is shown to be negligible.
doi:10.1090/s0025-5718-1992-1134713-7 fatcat:3of55mzzsvarbpnjesnyfddw24