论文信息 - Note on "A New Scaling for Newton's Iteration for the Polar Decomposition and Its Backward Stability" by R. Byers and H. Xu

Note on "A New Scaling for Newton's Iteration for the Polar Decomposition and Its Backward Stability" by R. Byers and H. Xu

We show that the proof of Theorem 4.5 in the paper by Byers and Xu is not complete for the considered class of matrices. The first order analysis is not applicable to the considered problem of rounding error propagation.

Krystyna Zietak | Andrzej Kielbasinski

[1] Ralph Byers,et al. A New Scaling for Newton's Iteration for the Polar Decomposition and its Backward Stability , 2008, SIAM J. Matrix Anal. Appl..

[2] Krystyna Zietak,et al. Numerical Behaviour of Higham's Scaled Method for Polar Decomposition , 2004, Numerical Algorithms.