Numerical methods for least squares problems / Åke Björck.

Format:

Book

Author/Creator:

Björck, Åke, 1934-

Contributor:

Society for Industrial and Applied Mathematics.

Language:

English

Subjects (All):

Equations, Simultaneous--Numerical solutions.

Equations, Simultaneous.

Least squares.

Physical Description:

1 online resource (408 p. )

Place of Publication:

Philadelphia, Pa. : Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1996.

Language Note:

English

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader.

Summary:

The method of least squares was discovered by Gauss in 1795. It has since become the principal tool to reduce 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. Least squares problems of large size are now routinely solved. Tremendous progress has been made in numerical methods for least squares problems, in particular for generalized and modified least squares problems and direct and iterative methods for sparse 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.

Contents:

Chapter 1. Mathematical and statistical properties of least squares solutions

Chapter 2. Basic numerical methods

Chapter 3. Modified least squares problems

Chapter 4. Generalized least squares problems

Chapter 5. Constrained least squares problems

Chapter 6. Direct methods for sparse least squares problems

Chapter 7. Iterative methods for least squares problems

Chapter 8. Least squares with special bases

Chapter 9. Nonlinear least squares problems

References

Bibliography.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references (p. 360-400) and index.

Title from title screen, viewed 04/05/2011.

ISBN:

1-61197-148-9

Publisher Number:

OT51 SIAM