On the Convergence of the QR Algorithm with Origin Shifts for Normal Matrices
C. P. Huang · IMA Journal of Numerical Analysis · 1981
We present in this paper some of the effects of the QR algorithm with origin shift on upper Hessenberg normal matrices. We also describe a theorem to show theoretically that if the QR algorithm is applied with appropriate origin shifts to an upper Hessenberg normal matrix, then the modulus of the (n, n−1)-element of the matrix approaches zero monotonically.