Numerical Methods for Least Square Problems

The method of least squares: the principal tool for reducing the influence of errors when fitting models to given observations.

Åke Björck (Author)

9780898713602, Society for Industrial and Applied Mathematics

Paperback / softback, published 31 December 1996

426 pages
25.1 x 17.5 x 2.2 cm, 0.762 kg

"Bjorck is an expert on least squares problems.…This volume surveys numerical methods for these problems. …its strength is in the detailed discussion of least squares problems and of their various solution techniques." -B. Borchers, CHOICE, Vol. 34, No. 3, November 1996.

The method of least squares was discovered by Gauss in 1795 and has since become the principal tool for reducing the influence of errors when fitting models to given observations. Today, applications of least squares arise in a great number of scientific areas, such as statistics, geodetics, signal processing, and control. In the last 20 years there has been a great increase in the capacity for automatic data capturing and computing and tremendous progress has been made in numerical methods for least squares problems. Until now there has not been a monograph that covers the full spectrum of relevant problems and methods in least squares. This volume gives an in-depth treatment of topics such as methods for sparse least squares problems, iterative methods, modified least squares, weighted problems, and constrained and regularized problems. The more than 800 references provide a comprehensive survey of the available literature on the subject.

Preface
1. Mathematical and statistical properties of least squares solutions
2. Basic numerical methods
3. Modified least squares problems
4. Generalized least squares problems
5. Constrained least squares problems
6. Direct methods for sparse problems
7. Iterative methods for least squares problems
8. Least squares problems with special bases
9. Nonlinear least squares problems
Bibliography
Index.

Subject Areas: Miscellaneous items [WZ]