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Numerical Linear Algebra for Applications in Statistics

  • Textbook
  • © 1998

Overview

Authors:
  1. James E. Gentle

    1. Institute for Computational Sciences and Informatics, George Mason University, Fairfax, USA

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Part of the book series: Statistics and Computing (SCO)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Computer Storage and Manipulation of Data

    • James E. Gentle
    Pages 1-45

  3. Basic Vector/Matrix Computations

    • James E. Gentle
    Pages 47-86

  4. Solution of Linear Systems

    • James E. Gentle
    Pages 87-121

  5. Computation of Eigenvectors and Eigenvalues and the Singular Value Decomposition

    • James E. Gentle
    Pages 123-135

  6. Software for Numerical Linear Algebra

    • James E. Gentle
    Pages 137-159

  7. Applications in Statistics

    • James E. Gentle
    Pages 161-182

  8. Back Matter

    Pages 183-221
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Keywords

About this book

Numerical linear algebra is one of the most important subjects in the field of statistical computing. Statistical methods in many areas of application require computations with vectors and matrices. This book describes accurate and efficient computer algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. An understanding of numerical linear algebra requires basic knowledge both of linear algebra and of how numerical data are stored and manipulated in the computer. The book begins with a discussion of the basics of numerical computations, and then describes the relevant properties of matrix inverses, matrix factorizations, matrix and vector norms, and other topics in linear algebra; hence, the book is essentially self- contained. The topics addressed in this bookconstitute the most important material for an introductory course in statistical computing, and should be covered in every such course. The book includes exercises and can be used as a text for a first course in statistical computing or as supplementary text for various courses that emphasize computations. James Gentle is University Professor of Computational Statistics at George Mason University. During a thirteen-year hiatus from academic work before joining George Mason, he was director of research and design at the world's largest independent producer of Fortran and C general-purpose scientific software libraries. These libraries implement many algorithms for numerical linear algebra. He is a Fellow of the American Statistical Association and member of the International Statistical Institute. He has held several national

Reviews

From a review:

JOURNAL OF AMERICAN STATISTICAL ASSOCIATION

"Gentle brings to this book (as well as his other recent books on further aspects of statistical computing) his vast knowledge and experience in the mathematics of scientific computing, the practical aspects of software development, and teaching. The presentation is exceptionally clear and well-sign-boarded. ...The writing style, though very precise, conveys a warmth and enthusiasm that will appeal to students."

 

Authors and Affiliations

  • Institute for Computational Sciences and Informatics, George Mason University, Fairfax, USA

    James E. Gentle

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