The Total Least Squares Problem – Computational Aspects and Analysis
Computational Aspects and Analysis

This book is devoted entirely to total least squares and the authors give a unified presentation of the TLS problem.

Sabine Van Huffel (Author), Joos Vandewalle (Author)

9780898712759

Paperback / softback, published 28 February 1992

311 pages
25.4 x 17.8 x 1.8 cm, 0.554 kg

"Van Huffel and Vandewalle provide a simple road map to the book for readers with different objectives, so that those with a problem to solve can locate relevant material quickly...Scientists and engineers looking for a way to learn the simple but powerful methods the TLS techniques provide for dealing with a variety of knotty problems in analyzing real data need look no farther than this book." -- George W. Fisher, Johns Hopkins University, Mathematics of Computation, October 1992, Vol. 59, No. 200.

This is the first book devoted entirely to total least squares. The authors give a unified presentation of the TLS problem. A description of its basic principles are given, the various algebraic, statistical and sensitivity properties of the problem are discussed, and generalizations are presented. Applications are surveyed to facilitate uses in an even wider range of applications. Whenever possible, comparison is made with the well-known least squares methods. A basic knowledge of numerical linear algebra, matrix computations, and some notion of elementary statistics is required of the reader; however, some background material is included to make the book reasonably self-contained.

Introduction
Basic principles of the total least squares problem
Extensions of the basic total least squares problem
Direct speed Improvement of the total least squares computations
Iterative speed Improvement for solving slowly varying total least squares problems
Algebraic Connections Between total least squares and least squares problems
Sensitivity analysis of total least squares and least squares problems in the presence of errors in all data
Statistical properties of the total least squares problem
Algebraic connections between total least squares estimation and classical linear regression in Multicollinearity problems
Conclusions.

Subject Areas: Miscellaneous items [WZ]