Scaling for Orthogonality
Abstract
In updating algorthms where orthogonal transformations are
accumulated, it is important to preserve the orthogonality of the
product in the presence of rounding error. Moonen, Van Dooren, and
Vandewalle have pointed out that simply normalizing the columns of the
product tends to preserve orthogonality\,---\,though not, as DeGroat
points out, to working precision. In this note we give an analysis of
the phenomenon.
(Also cross-referenced as UMIACS-TR-92-43)