2009/6/8 Robert Kern
Remember, the example is a **teaching** example.
I know. Honestly, I would prefer that teachers skip over the normal equations entirely and move directly to decomposition approaches. If you are going to make them implement least-squares from more basic tools, I think it's more enlightening as a student to start with the SVD than the normal equations.
I agree, and I wish our cirriculum followed that route. In linear algebra, I also don't much like the way eigenvalues are taught, where students have to solve characteristic polynomials by hand. When I teach the subject again, I'll pay more attention to these books: Numerical linear algebra by Lloyd Trefethen http://books.google.co.za/books?id=bj-Lu6zjWbEC (e.g. has SVD in Lecture 4) Applied Numerical Linear Algebra by James Demmel http://books.google.co.za/books?id=lr8cFi-YWnIC (e.g. has perturbation theory on page 4) Regards Stéfan