Author | Gentle, James E. author |
---|---|
Title | Numerical Linear Algebra for Applications in Statistics [electronic resource] / by James E. Gentle |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1998 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0623-1 |
Descript | XIII, 221 p. online resource |
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