Linear convergence in the shifted ๐๐ algorithm
Steve Batterson, David Day ยท Mathematics of Computation ยท 1992
Global and asymptotic convergence properties for the QR algorithm with Francis double shift are established for certain orthogonal similarity classes of 4 ร 4 4 \times 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.