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.

http://i.stanford.edu/pub/cstr/reports/cs/tr/76/559/CS-TR-76-559.pdf