Numerical Methods for Least Squares Problems

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Overview

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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Editorial Reviews

From the Publisher
'…This book, which was written by a celebrated person in the field, has become a monumental work … Altogether, very clearly written and a must for everyone who is interested in least squares, as well as all mathematics libraries.' Bob Matheij, ITW Nieuws

'…Until now there has not been a monograph covering the full spectrum of methods and applications in least squares. …This book is a great masterpiece that will serve as a reference for many years. It must be on the shelves of every numerical analyst, computational scientist and engineer, statistician and electrical engineer.' Claude Brejinski, Numerical Algorithms

'This monograph covers the full spectrum of relevant problems and up-to-date methods in least squares … a milestone in numerical linear algebra …' H. Späth, Zentrallblatt für Mathematik

' … The author has done a superb job of including the most recent research results, many of which are presented here for the first time in book form. The bibliography is comprehensive and contains more than eight hundred entries. The emphasis of the book is on linear least squares problems, but it also contains a chapter on surveying numerical methods for nonlinear problems.' Hongyuan Zha, Mathematical Reviews

'This book gives a very broad coverage of linear least squares problems. Detailed descriptions are provided for the best algorithms to use and the current literature, with some identification of software availability. No examples are given, and there are few graphs, but the detailed information about methods and algorithms makes this an excellent book … If you are going to solve a least squares problem of any magnitude, you need Numerical Methods for Least Squares Problems …' B. A. Finlayson, Applied Mechanics Review

"A comprehensive and up-to-date treatment that includes many recent developments. In addition to basic methods, it covers methods for modified and generalized least squares problems, and direct and iterative methods for sparse problems." -Arnold M. Ostebee, The American Mathematical Monthly, January 1997.

"Bjorck is an expert on least squares problems.…This volume surveys numerical methods for these problems. …its strength is in the detailed discussion of least squares problems and of their various solution techniques." -B. Borchers, CHOICE, Vol. 34, No. 3, November 1996.

Booknews
A textbook for an graduate or advanced undergraduate course in scientific computing and applied sciences, or a reference and tutorial for professionals in any of the many fields that use least squares to reduce errors when fitting a model to observations. Explains the numeral methods that have been developed over the past decade or two to solve such problems. Some of the material requires a solid understanding of numerical linear algebra. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Bob Matheij
This book, that was written by a celebrated person in the field, has become a monumental work. . Altogether, very clearly written and a must for everyone who is interested in least squares, as well as all mathematics libraries.
ITW Nieuws
B. Borchers
Bjorck is an expert on least squares problems. This volume surveys numerical methods for these problems. .its strength is in the detailed discussion of least squares problems and of their various solution techniques.
CHOICE
Arnold M. Ostebee
A comprehensive and up-to-date treatment that includes many recent developments. In addition to basic methods, it covers methods for modified and generalized least squares problems, and direct and iterative methods for sparse problems.
The American Mathematical Monthly
B. A. Finlayson
This book gives a very broad coverage of linear least squares problems. Detailed descriptions are provided for the best algorithms to use and the current literature, with some identification of software availability. No examples are given, and there are few graphs, but the detailed information about methods and algorithms makes this an excellent book. .If you are going to solve a least squares problem of any magnitude, you need Numerical Methods for Least Squares Problems.
— Applied Mechanics Review
Hongyuan Zha
The author has done a superb job of including the most recent research results, many of which are presented here for the first time in book form. The bibliography is comprehensive and contains more than eight hundred entries. The emphasis of the book is on linear least squares problems, but it also contains a chapter on surveying numerical methods for nonlinear problems
Mathematical Reviews
H. Spath
This monograph covers the full spectrum of relevant problems and up-to-date methods in least squares ...a milestone in numerical linear algebra.
Zentrallblatt für Mathematik
Claude Brejinski
Until now there has not been a monograph covering the full spectrum of methods and applications in least squares. ...This book is a great masterpiece that will serve as a reference for many years. It must be on the shelves of every numerical analyst, computational scientist and engineer, statistician and electrical engineer.
Numerical Algorithms
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Product Details

  • ISBN-13: 9780898713602
  • Publisher: SIAM
  • Publication date: 1/28/1996
  • Series: Miscellaneous Bks.
  • Edition description: New Edition
  • Pages: 408
  • Product dimensions: 6.70 (w) x 9.90 (h) x 0.90 (d)

Table of Contents

Preface; 1. Mathematical and statistical properties of least squares solutions; 2. Basic numerical methods; 3. Modified least squares problems; 4. Generalized least squares problems; 5. Constrained least squares problems; 6. Direct methods for sparse problems; 7. Iterative methods for least squares problems; 8. Least squares problems with special bases; 9. Nonlinear least squares problems; Bibliography; Index.
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