Report Number: CS-TR-76-559
Institution: Stanford University, Department of Computer Science
Title: Rank degeneracy and least squares problems
Author: Golub, Gene H.
Author: Klema, Virginia C.
Author: Stewart, Gilbert W.
Date: August 1976
Abstract: This paper is concerned with least squares problems when the
least squares matrix A is near a matrix that is not of full
rank. A definition of numerical rank is given. It is shown
that under certain conditions when A has numerical rank r
there is a distinguished r dimensional subspace of the column
space of A that is insensitive to how it is approximated by r
independent columns of A. The consequences of this fact for
the least squares problem are examined. Algorithms are
described for approximating the stable part of the column
space of A.