Numerical Linear Algebra for Applications in Statistics
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...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1998, 1998
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| Edition: | 1st ed. 1998 |
| Series: | Statistics and Computing
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 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