The Total Least Squares Problem: Computational Aspects and Analysisby Sabine van Huffel, Joos Vandewalle
Pub. Date: 01/28/1991
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.
Table of ContentsIntroduction; 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.
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