Solving Least Square Problems
Will be published approx. on 31. December 1995
Book
Paperback/Softback
349 pages
978-0-89871-356-5 (ISBN)
Description
An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. Numerical analysts, statisticians, and engineers have developed techniques and nomenclature for the least squares problems of their own discipline. This well-organized presentation of the basic material needed for the solution of least squares problems helps to unify this divergence of methods. Mathematicians, practicing engineers, and scientists will welcome its return to print.
The material covered includes Householder and Givens orthogonal transformations, the QR and SVD decompositions, equality constraints, solutions in nonnegative variables, banded problems, and updating methods for sequential estimation. Both the theory and practical algorithms are included. The easily understood explanations and the appendix providing a review of basic linear algebra make the book accessible for the nonspecialist.
This Classic edition includes a new appendix that summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method. The software has been upgraded to conform to the FORTRAN 77 standard and a new subroutine has been added in FORTRAN 90 for the solution of the bounded variables least squares problem (BVLS). The codes are available from netlib via the Internet.
The material covered includes Householder and Givens orthogonal transformations, the QR and SVD decompositions, equality constraints, solutions in nonnegative variables, banded problems, and updating methods for sequential estimation. Both the theory and practical algorithms are included. The easily understood explanations and the appendix providing a review of basic linear algebra make the book accessible for the nonspecialist.
This Classic edition includes a new appendix that summarizes the major developments since the book was originally published in 1974. The additions are organized in short sections associated with each chapter. An additional 230 references have been added, bringing the bibliography to over 400 entries. Appendix C has been edited to reflect changes in the associated software package and software distribution method. The software has been upgraded to conform to the FORTRAN 77 standard and a new subroutine has been added in FORTRAN 90 for the solution of the bounded variables least squares problem (BVLS). The codes are available from netlib via the Internet.
More details
Series
Edition
Revised edition
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 20 mm
Weight
476 gr
ISBN-13
978-0-89871-356-5 (9780898713565)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
Preface to the Classics Edition
Preface
Chapter 1: Introduction
Chapter 2: Analysis of the Least Squares Problem
Chapter 3: Orthogonal Decomposition by Certain Elementary Orthogonal Transformations
Chapter 4: Orthogonal Decomposition by Singular Value Decomposition
Chapter 5: Perturbation Theorems for Singular Values
Chapter 6: Bounds for the Condition Number of a Triangular Matrix
Chapter 7: The Pseudoinverse
Chapter 8: Perturbation Bounds for the Pseudoinverse
Chapter 9: Perturbation Bounds for the Solution of Problem LS
Chapter 10: Numerical Computations Using Elementary Orthogonal Transformations
Chapter 11: Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem
Chapter 12: Computation of the Covariance Matrix of the Solution Parameters
Chapter 13: Computing the Solution for the Underdetermined Full Rank Problem
Chapter 14: Computing the Solution for Problem LS with Possibly Deficient Pseudorank
Chapter 15: Analysis of Computing Errors for Householder Transformations
Chapter 16: Analysis of Computing Errors for the Problem LS
Chapter 17: Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic
Chapter 18: Computation of the Singular Value Decomposition and the Solution of Problem LS
Chapter 19: Other Methods for Least Squares Problems
Chapter 20: Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space
Chapter 21: Linear Least Squares with Linear Equality Constraints by Direct Elimination
Chapter 22: Linear Least Squares with Linear Equality Constraints by Weighting
Chapter 23: Linear Least Squares with Linear Inequality Constraints
Chapter 24: Modifying a QR Decomposition to Add or Remove Column Vectors
Chapter 25: Practical Analysis of Least Squares Problems
Chapter 26: Examples of Some Methods of Analyzing a Least Squares Problem
Chapter 27: Modifying a QR Decomposition to Add or Remove Row Vectors with Application to Sequential Processing of Problems Having a Large or Banded Coefficient Matrix
Appendix A: Basic Linear Algebra Including Projections
Appendix B: Proof of Global Quadratic Convergence of the QR Algorithm
Appendix C: Description and Use of FORTRAN Codes for Solving Problem LS
Appendix D: Developments from 1974 to 1995
Bibliography
Index.
Preface
Chapter 1: Introduction
Chapter 2: Analysis of the Least Squares Problem
Chapter 3: Orthogonal Decomposition by Certain Elementary Orthogonal Transformations
Chapter 4: Orthogonal Decomposition by Singular Value Decomposition
Chapter 5: Perturbation Theorems for Singular Values
Chapter 6: Bounds for the Condition Number of a Triangular Matrix
Chapter 7: The Pseudoinverse
Chapter 8: Perturbation Bounds for the Pseudoinverse
Chapter 9: Perturbation Bounds for the Solution of Problem LS
Chapter 10: Numerical Computations Using Elementary Orthogonal Transformations
Chapter 11: Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem
Chapter 12: Computation of the Covariance Matrix of the Solution Parameters
Chapter 13: Computing the Solution for the Underdetermined Full Rank Problem
Chapter 14: Computing the Solution for Problem LS with Possibly Deficient Pseudorank
Chapter 15: Analysis of Computing Errors for Householder Transformations
Chapter 16: Analysis of Computing Errors for the Problem LS
Chapter 17: Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic
Chapter 18: Computation of the Singular Value Decomposition and the Solution of Problem LS
Chapter 19: Other Methods for Least Squares Problems
Chapter 20: Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space
Chapter 21: Linear Least Squares with Linear Equality Constraints by Direct Elimination
Chapter 22: Linear Least Squares with Linear Equality Constraints by Weighting
Chapter 23: Linear Least Squares with Linear Inequality Constraints
Chapter 24: Modifying a QR Decomposition to Add or Remove Column Vectors
Chapter 25: Practical Analysis of Least Squares Problems
Chapter 26: Examples of Some Methods of Analyzing a Least Squares Problem
Chapter 27: Modifying a QR Decomposition to Add or Remove Row Vectors with Application to Sequential Processing of Problems Having a Large or Banded Coefficient Matrix
Appendix A: Basic Linear Algebra Including Projections
Appendix B: Proof of Global Quadratic Convergence of the QR Algorithm
Appendix C: Description and Use of FORTRAN Codes for Solving Problem LS
Appendix D: Developments from 1974 to 1995
Bibliography
Index.