Numerical Linear Algebra for Applications in Statistics

Linear algebra is one of the most imprortant mathematical and computational tools in the sciences. A knowledge of linear algebra is essential for research in statistics or the application of statistics. This book presents the aspects of numerical linear algebra that are important to statisticians.

Zusammenfassung

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."

Inhalt
1 Computer Storage and Manipulation of Data.- 1.1 Digital Representation of Numeric Data.- 1.2 Computer Operations on Numeric Data.- 1.3 Numerical Algorithms and Analysis.- Exercises.- 2 Basic Vector/Matrix Computations.- 2.1 Notation, Definitions, and Basic Properties.- 2.2 Computer Representations and Basic Operations.- Exercises.- 3 Solution of Linear Systems.- 3.1 Gaussian Elimination.- 3.2 Matrix Factorizations.- 3.3 Iterative Methods.- 3.4 Numerical Accuracy.- 3.5 Iterative Refinement.- 3.6 Updating a Solution.- 3.7 Overdetermined Systems; Least Squares.- 3.8 Other Computations for Linear Systems.- Exercises.- 4 Computation of Eigenvectors and Eigenvalues and the Singular Value Decomposition.- 4.1 Power Method.- 4.2 Jacobi Method.- 4.3 QR Method for Eigenanalysis.- 4.4 Singular Value Decomposition.- Exercises.- 5 Software for Numerical Linear Algebra.- 5.1 Fortran and C.- 5.2 Interactive Systems for Array Manipulation.- 5.3 High-Performance Software.- 5.4 Test Data.- Exercises.-6 Applications in Statistics.- 6.1 Fitting Linear Models with Data.- 6.2 Linear Models and Least Squares.- 6.3 Ill-Conditioning in Statistical Applications.- 6.4 Testing the Rank of a Matrix.- 6.5 Stochastic Processes.- Exercises.- Appendices.- A Notation and Definitions.- B Solutions and Hints for Selected Exercises.- Literature in Computational Statistics.- World Wide Web, News Groups, List Servers, and Bulletin Boards.- References.- Author Index.