V-invariant methods for generalised least squares problems

Research Report MRR01-024

V-invariant methods for generalised least squares problems

M.R. Osborne

Abstract: An important consideration in generalised least squares problems is that the dimension of the covariance matrix V is the dimension of the data set and is large when the data set is large. Also, the problem solution can be well determined in cases where V is illconditioned or singular. Here aspects of a class of methods which factorize the design matrix while leaving V invariant, and which can be expected to be well behaved exactly when the original problem solution is well behaved, are considered. Implementation is most satisfactory when V is diagonal. This can be achieved by a preprocessing step in which V is replaced by the diagonal matrix D which results from the modified Cholesky factorization PVP^T->LDL^T where L is unit lower triangular and P is the permutation matrix associated with diagonal pivoting. Conditions under which this replacement is satisfactory are investigated.

Download paper:

PDF file (107K)

This service is maintained by the Mathematical Sciences Institute (MSI)
Comments to webmaster@maths.anu.edu.au URL: http://wwwmaths.anu.edu.au/