38.9 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) http://pdg.lbl.gov/

The Review of Particle Physics is available online at the website given above.

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, pp. 152-154.

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.