38.13 References and Further Reading
A summary of formulas and techniques for least squares fitting can be
found in the “Statistics” chapter of the Annual Review of Particle
Physics prepared by the Particle Data Group,
- Review of Particle Properties,
R.M. Barnett et al., Physical Review D54, 1 (1996)
The Review of Particle Physics is available online at the website given
The tests used to prepare these routines are based on the NIST
Statistical Reference Datasets. The datasets and their documentation are
available from NIST at the following website,
More information on Tikhonov regularization can be found in
- Hansen, P. C. (1998), Rank-Deficient and Discrete Ill-Posed Problems:
Numerical Aspects of Linear Inversion. SIAM Monogr. on Mathematical
Modeling and Computation, Society for Industrial and Applied Mathematics
- M. Rezghi and S. M. Hosseini (2009), A new variant of L-curve for
Tikhonov regularization, Journal of Computational and Applied Mathematics,
Volume 231, Issue 2, pages 914-924.
The GSL implementation of robust linear regression closely follows the publications
- DuMouchel, W. and F. O’Brien (1989), "Integrating a robust
option into a multiple regression computing environment,"
Computer Science and Statistics: Proceedings of the 21st
Symposium on the Interface, American Statistical Association
- Street, J.O., R.J. Carroll, and D. Ruppert (1988), "A note on
computing robust regression estimates via iteratively
reweighted least squares," The American Statistician, v. 42,
More information about the normal equations and TSQR approach for solving
large linear least squares systems can be found in the publications
- Trefethen, L. N. and Bau, D. (1997), "Numerical Linear Algebra", SIAM.
- Demmel, J., Grigori, L., Hoemmen, M. F., and Langou, J.
"Communication-optimal parallel and sequential QR and LU factorizations",
UCB Technical Report No. UCB/EECS-2008-89, 2008.