Solving Least Squares Problems - Brossura

Lawson, Charles L.; Hanson, Richard J.

Brossura

ISBN 10: 0898713560 ISBN 13: 9780898713565

Casa editrice: Society for Industrial and Applied Mathematics, 1987

Riassunto

An accessible text for the study of numerical methods for solving least squares problems remains an essential part of a scientific software foundation. This book has served this purpose well. 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 can unify this divergence of methods. Mathematicians, practising 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 non-specialist.

Su questo libro

Descrizione del libro:

This Classic edition includes a new appendix which 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.

Contenuti:

Preface to the Classics Edition; Preface; 1. Introduction; 2. Analysis of the Least Squares Problem; 3. Orthogonal Decomposition by Certain Elementary Orthogonal Transformations; 4. Orthogonal Decomposition by Singular Value Decomposition; 5. Perturbation Theorems for Singular Values; 6. Bounds for the Condition Number of a Triangular Matrix; 7. The Pseudoinverse; 8. Perturbation Bounds for the Pseudoinverse; 9. Perturbation Bounds for the Solution of Problem LS; 10. Numerical Computations Using Elementary Orthogonal Transformations; 11. Computing the Solution for the Overdetermined or Exactly Determined Full Rank Problem; 12. Computation of the Covariance Matrix of the Solution Parameters; 13. Computing the Solution for the Underdetermined Full Rank Problem; 14. Computing the Solution for Problem LS with Possibly Deficient Pseudorank; 15. Analysis of Computing Errors for Householder Transformations; 16. Analysis of Computing Errors for the Problem LS; 17. Analysis of Computing Errors for the Problem LS Using Mixed Precision Arithmetic; 18. Computation of the Singular Value Decomposition and the Solution of Problem LS; 19. Other Methods for Least Squares Problems; 20. Linear Least Squares with Linear Equality Constraints Using a Basis of the Null Space; 21. Linear Least Squares with Linear Equality Constraints by Direct Elimination; 22. Linear Least Squares with Linear Equality Constraints by Weighting; 23. Linear Least Squares with Linear Inequality Constraints; 24. Modifying a QR Decomposition to Add or Remove Column Vectors; 25. Practical Analysis of Least Squares Problems; 26. Examples of Some Methods of Analyzing a Least Squares Problem; 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.

Su questa edizione

• Editore: Society for Industrial and Applied Mathematics
• Data di pubblicazione: 1987
• ISBN 10: 0898713560
• ISBN 13: 9780898713565
• Rilegatura: Copertina flessibile
• Numero di pagine: 350