Least Squares Data Fitting with Applications

Least Squares Data Fitting with Applications

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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, VAsctor 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. Included area€c an overview of computational methods together with their properties and advantagesa€c topics from statistical regression analysis that help readers to understand and evaluate the computed solutionsa€c many examples that illustrate the techniques and algorithms Least Squares Data Fitting with Applications can be used as a textbook for advanced undergraduate or graduate courses and professionals in the sciences and in engineering. -- Stephen Wright, University of Wisconsin'Then it is easy to see that for the un-weighted data fitting problem we have the relations r=yaˆ’Ax and I(x)= maˆ‘ i=1 ri(x)2= r22= yaˆ’Ax22. Similarly, ... For the data fitting problem in Example 2, we try both the polynomial fit and the trigonometric fit.

Title:Least Squares Data Fitting with Applications
Author: Per Christian Hansen, Víctor Pereyra, Godela Scherer
Publisher:JHU Press - 2012-12-14

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