Scientific Computing and Matrix Computations Seminar: A Backward Error Formula for the Global Least-Squares Problem
Seminar: Scientific Computing: CS | May 8 | 2-3 p.m. | 380 Soda Hall
Eric Hallman, UCB
In this talk we present formulas for the normwise backward error for the problems AX=B and min_X ||AX-B||_F, extending the results of Walden/Karlson/Sun (1998) and Sun/Sun (1997) to systems with multiple right hand sides. These formulas are valid for matrices of any dimension and rank. We also propose two estimates that numerical experiments suggest are highly reliable, one of which may be interpreted as an extension of an estimate for the least-square backward error by Karlson and Walden (1997). Proving the general reliability of these estimates remains an open problem, but we do so for a few special cases.