[PDF] A Practical Guide To The Method Of Least Squares eBook

Author : Tilo Strutz
Publisher : Springer Vieweg
Page : 0 pages
File Size : 31,16 MB
Release : 2015-12-16
Category : Technology & Engineering
ISBN : 9783658114558

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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

Author : Willie Chee Keong Tan
Publisher : World Scientific
Page : 312 pages
File Size : 18,10 MB
Release : 2022-04-27
Category : Science
ISBN : 9811256950

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Research Methods: A Practical Guide for Students and Researchers is a practical guide on how to conduct research systematically and professionally. The book begins by distinguishing between causal and interpretive sciences. It then guides the reader on how to formulate the research question, review the literature, develop the hypothesis or framework, select a suitable research methodology, and analyze both quantitative and qualitative data.The book uses classic examples as exemplars. It also uses many examples from different disciplines and sectors to demonstrate and showcase the inter-connections and wider applications of research tools.The book emphasizes integration. It does not merely provide a smorgasbord of research designs, data collection methods, and ways to analyze data. Instead, it shows how one could formulate research strategies given the outcomes the researchers are required or tasked to deliver.The revised edition includes three new chapters on time series (including spatial models), machine learning, and meta-analysis. In addition, existing chapters have been expanded to include more examples, digital research, and new material.

Author : Dana Prescott Bartlett
Publisher : Kessinger Publishing
Page : 160 pages
File Size : 46,41 MB
Release : 2008-10-01
Category : Law
ISBN : 9781437059618

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This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

Author : Bruce P. Gibbs
Publisher : John Wiley & Sons
Page : 559 pages
File Size : 15,16 MB
Release : 2011-03-29
Category : Technology & Engineering
ISBN : 1118003160

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This book is intended primarily as a handbook for engineers who must design practical systems. Its primary goal is to discuss model development in sufficient detail so that the reader may design an estimator that meets all application requirements and is robust to modeling assumptions. Since it is sometimes difficult to a priori determine the best model structure, use of exploratory data analysis to define model structure is discussed. Methods for deciding on the “best” model are also presented. A second goal is to present little known extensions of least squares estimation or Kalman filtering that provide guidance on model structure and parameters, or make the estimator more robust to changes in real-world behavior. A third goal is discussion of implementation issues that make the estimator more accurate or efficient, or that make it flexible so that model alternatives can be easily compared. The fourth goal is to provide the designer/analyst with guidance in evaluating estimator performance and in determining/correcting problems. The final goal is to provide a subroutine library that simplifies implementation, and flexible general purpose high-level drivers that allow both easy analysis of alternative models and access to extensions of the basic filtering. Supplemental materials and up-to-date errata are downloadable at http://booksupport.wiley.com.

Author : Per Christian Hansen
Publisher : JHU Press
Page : 325 pages
File Size : 23,36 MB
Release : 2013-01-15
Category : Mathematics
ISBN : 1421408589

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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.

Author : Paul Gemperline
Publisher : CRC Press
Page : 552 pages
File Size : 29,21 MB
Release : 2006-04-16
Category : Mathematics
ISBN : 1420018302

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The limited coverage of data analysis and statistics offered in most undergraduate and graduate analytical chemistry courses is usually focused on practical aspects of univariate methods. Drawing in real-world examples, Practical Guide to Chemometrics, Second Edition offers an accessible introduction to application-oriented multivariate meth