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. Included are • an overview of computational methods together with their properties and advantages • topics from statistical regression analysis that help readers to understand and evaluate the computed solutions • 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.

A least-squares method for calculating coefficients from a linear differential equation directly from transient-response data is presented. Examples illustrating the application of the method to the calculation of aircraft-stability parameters from the airplane response of an elevator deflection are given.

The subject of data fitting bridges many disciplines, especially those traditionally dealing with statistics like physics, mathematics, engineering, biology, economy, or psychology, but also more recent fields like computer vision. This book addresses itself to engineers and computer scientists or corresponding undergraduates who are interested in data fitting by the method of least-squares approximation, but have no or only limited pre-knowledge in this field. Experienced readers will find in it new ideas or might appreciate the book as a useful work of reference. Familiarity with basic linear algebra is helpful though not essential as the book includes a self-contained introduction and presents the method in a logical and accessible fashion. The primary goal of the text is to explain how data fitting via least squares works. The reader will find that the emphasis of the book is on practical matters, not on theoretical problems. In addition, the book enables the reader to design own software implementations with application-specific model functions based on the comprehensive discussion of several examples. The text is accompanied with working source code in ANSI-C for fitting with weighted least squares including outlier detection. Among others the book covers following topics * fitting of linear and nonlinear functions with one- or multi-dimensional variables * weighted least-squares * outlier detection * evaluation of the fitting results * different optimisation strategies * combined fitting of different model functions * total least-squares approach with multi-dimensional conditions

Develops the full power of the least-squares method Enables engineers and scientists to apply the method to their specific problem Deals with linear as well as with non-linear least-squares, parametric as well as non-parametric methods

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.

Data Fitting in the Chemical Sciences Peter Gans, School of Chemistry, The University of Leeds, Leeds, UK Data fitting is a technique of central importance in modern experimental science. It is the means by which data is tested against a model of the experimental system, be it a theoretical or empirical model. In this book an all-round approach is adopted in which the first stage of data-fitting is seen as data collection, the second is numerical processing and the third a critical evaluation of the 'goodness' of fit in both statistical and common sense terms. Each stage is considered in detail: the sources and nature of experimental errors; the theory of least-squares fitting; probability theory; hypothesis testing, and the application of scientific criteria. The theory is complemented by three chapters on a wide range of applications. The emphasis of this book is on methodology: why certain procedures are preferred rather than how any one procedure is implemented. The author aims to assist people in extracting from their data its full information content, i.e. to use their data, not abuse it.

"Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision a"

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Intended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.