Computer solution and perturbation analysis of generalized linear least squares problems

Author:
C. C. Paige

Journal:
Math. Comp. **33** (1979), 171-183

MSC:
Primary 65D10; Secondary 65F35

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514817-3

MathSciNet review:
514817

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A new formulation of the generalized linear least squares problem is given. This is based on some ideas in estimation and allows complete generality in that there are no restrictions on the matrices involved. The formulation leads directly to a numerical algorithm involving orthogonal decompositions for solving the problem. A perturbation analysis of the problem is obtained by using the new formulation and some of the decompositions used in the solution. A rounding error analysis is given to show that the algorithm is numerically stable.

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Additional Information

Keywords:
Covariance matrices,
error analysis,
estimation of linear systems,
linear least squares,
matrix computations,
perturbation analysis,
regression analysis

Article copyright:
© Copyright 1979
American Mathematical Society