An asymptotic behavior of QR decomposition

The m-th root of the diagonal of the upper triangular matrix Rm in the QR decomposition of AXmB = QmRm converges and the limit is given by the moduli of the eigenvalues of X with some ordering, where A,B,X∈Cn×n are nonsingular. The asymptotic behavior of the strictly upper triangular part of Rm is discussed. Some computational experiments are discussed.