by **sven** » Mon Jan 29, 2007 4:43 pm

Jim Demmel reminded me that if you column scale A by powers of the radix,

(and ignoring over/underflow and Strassen-BLAS), then the roundoff errors from QR (without column pivoting) and subsequently solving the least squares problem are invariant? The scale factors don't affect Q, just scale the columns of R, and just "factor out" of the triangular solve.

But when solving the least squares problem with pivoting, or with any orthogonal transformation from the right, such as in the SVD, column scaling can be important. It could change the condition estimate arbitrarily, if the

columns are badly scaled, so that the scaled solution could have a much smaller normwise error bound than the unscaled solution.

We hope to include some advice in a future edition of the Users' Guide.

Jim and Sven.