Numerical Methods for Least Squares Problems

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SIAM, Dec 1, 1996 - Mathematics - 408 pages
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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.
  

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The Best available resource on the least squares technique...
both theory and applications.

Contents

Basic Numerical Methods
37
Modified Least Squares Problems
127
Generalized Least Squares Problems
153
Constrained Least Squares Problems
187
Direct Methods for Sparse Problems
215
Iterative Methods For Least Squares Problems
269
Least Squares Problems with Special Bases
317
Nonlinear Least Squares Problems
339
Bibliography
359
Index
401
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