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The total least squares problem: computational aspects and analysis

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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.

Author(s): Sabine Van Huffel, Joos Vandewalle
Series: Frontiers in applied mathematics 9
Publisher: Society for Industrial and Applied Mathematics
Year: 1987

Language: English
Pages: 315
City: Philadelphia

The Total Least Squares Problem: Computational Aspects and Analysis......Page 2
ISBN 0-89871-275-0......Page 5
Contents......Page 8
Foreword......Page 10
Preface......Page 12
1 Introduction......Page 16
2 Basic Principles of the Total Least Squares Problem......Page 42
3 Extensions of the Basic Total Least Squares Problem......Page 64
4 Direct Speed Improvement of the Total Least Squares Computations......Page 112
5 Iterative Speed Improvement for Solving Slowly Varying Total Least Squares Problems......Page 140
6 Algebraic Connections Between Total Least Squares and Least Squares Problems......Page 196
7 Sensitivity Analysis of Total Least Squares and Least Squares Problems in the Presence of Errors in all Data......Page 214
8 Statistical Properties of the Total Least Squares Problem......Page 242
9 Algebraic Connections Between Total Least Squares Estimation and Classical Linear Regression in Multicollinearity Problems......Page 266
10 Conclusions......Page 278
References......Page 300
Index......Page 312