Gene Golub Symposium
The Backward Error Analysis Dogma
Robert Skeel, Purdue University
Backward error analysis is a useful concept in numerical computing. Its descriptive role is mentioned in the book by Golub and Van Loan. However, other authors have gone further to make backward error analysis prescriptive: they define numerical stability to mean that the computed solution is the exact solution of a slightly different problem. This is wrong-headed for two reasons: first, there are technical difficulties; second, it is inconsistent with the actual purpose of computation. There are alternative approaches that are superior, and these are described. If time permits, other ill-conceived ideas in numerical linear algebra will be discussed.
