The Total Least Squares Problem: Computational Aspects and Analysis(9 Frontiers in Applied Mathematics)

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 Contents:
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.

Review :
'The authors succeed in conveying to the reader through examples and references that TLS is applicable to a wide variety of applications, such as in signal processing or system identification. Also, computational aspects of various direct and iterative algorithms are investigated, and statistical properties of TLS are presented. The 300 pages in this book represent the first comprehensive treatment of TLS, and it should prove to be a valuable reference book to anyone whose work involves solving LS and TLS problems.' Ricardo D. Fierro, SIAM Review 'This is an excellent book which fills the need for a global approach to the problems of linear parameter estimation. The authors have wide experience in advising workers in diverse fields on the use of their algorithms. They have presented their work in a clear and concise manner, using standard mathematical ideas.' R .P. Tewarson, Mathematical Reviews ' ... a comprehensive and up-to-date treatment of rigorous mathematical analysis, computational methods and applications of the TLS problems.' Zhaojun Bai, I.M.A.G.E (ILAS) ' ... lucid and well organized monograph ... the authors do an excellent job of relating the ordinary least squares and total least squares approaches, surveying numerical - analytic measures of sensitivity for least squares and total least squares solutions, and outlining large-sample statistical properties of the total least squares solutions. Their monograph thus provides a broad and very useful interdisciplinary overview of an important class of problems.' L. J. Gleser, Short Book Reviews ' ... TLS (Total Least Squares) represents a technique that synthesizes statistical and numerical methodologies for solving problems arising in many application areas. The authors of this monograph have been leaders in showing how to use TLS for solving a variety of problems, especially those arising in a signal processing context. They give an elegant presentation of the various aspects of the TLS problem. Their survey encompasses the many elements required to understand the problem. It is a pleasure to read such a clear account, which is presented using standard mathematical ideas and nomenclature.' Gene H. Golub, Stanford University "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.