@inproceedings{76eebed07e464fd1aefd6ae20d732324,
title = "V-invariant methods for generalised least squares problems",
abstract = "An important consideration in solving generalised least squares problems is the dimension of the covariance matrix V. This has the dimension of the data set and is large when the data set is large. In addition the problem can be formulated to have a well determined solution in cases where V is illconditioned or singular, a class of problems that includes the case of equality constrained least squares. This paper considers a class of methods which factorize the design matrix A while leaving V invariant, and which can be expected to be well behaved exactly when the original problem solution is well behaved. 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 PVPT → LDLT 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.",
author = "Osborne, {M. R.}",
year = "2003",
doi = "10.1007/3-540-44863-2_66",
language = "English",
isbn = "9783540401964",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "673--682",
editor = "Sloot, {Peter M.A.} and David Abramson and Bogdanov, {Alexander V.} and Gorbachev, {Yuriy E.} and Dongarra, {Jack J.} and Zomaya, {Albert Y.}",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
address = "Germany",
edition = "Peer Reviewed",
note = "International Conference on Computational Science (ICCS 2003) ; Conference date: 01-01-2003",
}