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Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.
This book explains how computer software is designed to perform the tasks required for sophisticated statistical analysis. For statisticians, it examines the nitty-gritty computational problems behind statistical methods. For mathematicians and computer scientists, it looks at the application of mathematical tools to statistical problems. The first half of the book offers a basic background in numerical analysis that emphasizes issues important to statisticians. The next several chapters cover a broad array of statistical tools, such as maximum likelihood and nonlinear regression. The author also treats the application of numerical tools; numerical integration and random number generation are explained in a unified manner reflecting complementary views of Monte Carlo methods. Each chapter contains exercises that range from simple questions to research problems. Most of the examples are accompanied by demonstration and source code available from the author's website. New in this second edition are demonstrations coded in R, as well as new sections on linear programming and the Nelder–Mead search algorithm.
Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background.
Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.
A graduate-level introduction balancing theory and application, providing full coverage of classical methods with many practical examples and demonstration programs.
At last—a social scientist's guide through the pitfalls of modern statistical computing Addressing the current deficiency in the literature on statistical methods as they apply to the social and behavioral sciences, Numerical Issues in Statistical Computing for the Social Scientist seeks to provide readers with a unique practical guidebook to the numerical methods underlying computerized statistical calculations specific to these fields. The authors demonstrate that knowledge of these numerical methods and how they are used in statistical packages is essential for making accurate inferences. With the aid of key contributors from both the social and behavioral sciences, the authors have assembled a rich set of interrelated chapters designed to guide empirical social scientists through the potential minefield of modern statistical computing. Uniquely accessible and abounding in modern-day tools, tricks, and advice, the text successfully bridges the gap between the current level of social science methodology and the more sophisticated technical coverage usually associated with the statistical field. Highlights include: A focus on problems occurring in maximum likelihood estimation Integrated examples of statistical computing (using software packages such as the SAS, Gauss, Splus, R, Stata, LIMDEP, SPSS, WinBUGS, and MATLAB®) A guide to choosing accurate statistical packages Discussions of a multitude of computationally intensive statistical approaches such as ecological inference, Markov chain Monte Carlo, and spatial regression analysis Emphasis on specific numerical problems, statistical procedures, and their applications in the field Replications and re-analysis of published social science research, using innovative numerical methods Key numerical estimation issues along with the means of avoiding common pitfalls A related Web site includes test data for use in demonstrating numerical problems, code for applying the original methods described in the book, and an online bibliography of Web resources for the statistical computation Designed as an independent research tool, a professional reference, or a classroom supplement, the book presents a well-thought-out treatment of a complex and multifaceted field.
This book presents the central ideas of modern numerical analysis in a vivid and straightforward fashion with a minimum of fuss and formality. Stewart designed this volume while teaching an upper-division course in introductory numerical analysis. To clarify what he was teaching, he wrote down each lecture immediately after it was given. The result reflects the wit, insight, and verbal craftmanship which are hallmarks of the author. Simple examples are used to introduce each topic, then the author quickly moves on to the discussion of important methods and techniques. With its rich mixture of graphs and code segments, the book provides insights and advice that help the reader avoid the many pitfalls in numerical computation that can easily trap an unwary beginner. Written by a leading expert in numerical analysis, this book is certain to be the one you need to guide you through your favorite textbook.
Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.
Statistics and computing share many close relationships. Computing now permeates every aspect of statistics, from pure description to the development of statistical theory. At the same time, the computational methods used in statistical work span much of computer science. Elements of Statistical Computing covers the broad usage of computing in statistics. It provides a comprehensive account of the most important computational statistics. Included are discussions of numerical analysis, numerical integration, and smoothing. The author give special attention to floating point standards and numerical analysis; iterative methods for both linear and nonlinear equation, such as Gauss-Seidel method and successive over-relaxation; and computational methods for missing data, such as the EM algorithm. Also covered are new areas of interest, such as the Kalman filter, projection-pursuit methods, density estimation, and other computer-intensive techniques.
"This book is appropriate for an applied numerical analysis course for upper-level undergraduate and graduate students as well as computer science students. Actual programming is not covered, but an extensive range of topics includes round-off and function evaluation, real zeros of a function, integration, ordinary differential equations, optimization, orthogonal functions, Fourier series, and much more. 1989 edition"--Provided by publisher.