Numerical Linear Algebra for Applications in Statistics

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. Language: English