Sur lʼusage de la formule de Cauchy–Binet dans les démonstrations de convergence de lʼalgorithme QR tri-diagonal avec décalages

Abstract

Using the Cauchy–Binet formula, one shows that it is possible to simplify the convergence proofs of the tridiagonal QR algorithm with shifts due to Wilkinson (1968) [12], Hoffmann–Parlett (1978, 1998) [3,7], and Jiang–Zhang (1985) [4], including the quadratic or cubic convergence results.