Accuracy and Stability of Numerical Algorithms:
by
Nicholas J. Higham, SIAM,
January 1996.
Progress on Research Problems
Problem 20.2 on the backward error for the minimal 2-norm solution to
an underdetermined system has been solved
by Ji-guang Sun (Umea University) and
Zheng Sun (Linkoping University).
See
-
Ji-guang Sun and Zheng Sun.
Optimal backward perturbation bounds for underdetermined systems.
SIAM J. Matrix Anal. Appl., 18(2): 393-402, 1997.
Errors
The constant in (9.7) should be $\gamma_{3n}$ instead of $2\gamma_n$.
The inequality at the top of page 176 is incorrect because it
requires commutativity of diagonal matrices with full ones.
The constant in (10.6) should be $\gamma_{3n+1}$ instead of $2\gamma_{n+1}$.