Per Christian Hansen, Víctor Pereyra, and Godela Scherer
Johns Hopkins University Press 02
"Least squares remains a key topic in scientific computing, serving as a vital bridge between data and models. This book describes many interesting aspects of this problem class, including its statistical foundations, algorithms for solving both linear and nonlinear models, and its applications to many disciplines. The authors convey both the rich history of the subject and its ongoing importance."
—Stephen Wright, University of Wisconsin–Madison
A lucid explanation of the intricacies of both simple and complex least squares methods.
As one of the classical statistical regression techniques, and often the first to be taught to new students, least squares fitting can be a very effective tool in data analysis. Given measured data, we establish a relationship between independent and dependent variables so that we can use the data predictively. The main concern of Least Squares Data Fitting with Applications is how to do this on a computer with efficient and robust computational methods for linear and nonlinear relationships. The presentation also establishes a link between the statistical setting and the computational issues.
In a number of applications, the accuracy and efficiency of the least squares fit is central, and Per Christian Hansen, Víctor Pereyra, and Godela Scherer survey modern computational methods and illustrate them in fields ranging from engineering and environmental sciences to geophysics. Anyone working with problems of linear and nonlinear least squares fitting will find this book invaluable as a hands-on guide, with accessible text and carefully explained problems.
• an overview of computational methods together with their properties and advantages
• topics from statistical regression analysis that help readers to understand and valuate the computed solutions
• many examples that illustrate the techniques and algorithms
This book can be used as a textbook for advanced undergraduate or graduate level courses and as a reference book for professionals in the sciences and engineering.
About the Authors
Per Christian Hansen is a professor of scientific computing at the Technical University of Denmark.
Víctor Pereyra is a consulting professor of energy resources engineering at Stanford University and was a principal at Weidlinger Associates, Los Altos, California.
Godela Scherer is a visiting research fellow in the Department of Mathematics at the University of Reading, United Kingdom, and a professor of scientific computing at the Universidad Simón Bolívar, Venezuela.
Symbols and Acronyms;
1: The Linear Data Fitting Problem;
2: The Linear Least Squares Problem;
3: Analysis of the Least Squares Problems;
4: Direct Methods for Full-Rank Problems;
5: Direct Methods for Rank-Deficient Problems;
6: Methods for Large-Scale Problems;
7: Additional Topics in Least Squares;
8: Nonlinear Least Squares Problems;
9: Algorithms for Solving Nonlinear LSQ Problems;
10: Ill-Conditioned Problems;
11: Linear Least Squares Applications;
12: Nonlinear Least Squares Applications;
Appendix A: Sensitivity Analysis;
Appendix B: Linear Algebra Background;
Appendix C: Advanced Calculus Background;
Appendix D: Statistics;
To request an examination copy or desk copy of this book, please use our online request form at www.siam.org/catalog/adopt.php.
Least Squares; Data Fitting; Numerical algorithms; Linear and Nonlinear Regression; Applications.
2013 / xv + 305 pages / Hardcover / ISBN 978-1-4214-0786-9
List Price $85.00 / SIAM Member Price $59.50 / Order Code JH02