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Numerical linear algebra for applications in statistics

Numerical linear algebra for applications in statistics

자료유형
단행본
개인저자
Gentle, James E., 1943-.
서명 / 저자사항
Numerical linear algebra for applications in statistics / James E. Gentle.
발행사항
New York :   Springer,   c1998.  
형태사항
xiii, 221 p. : ill. ; 24 cm.
총서사항
Statistics and computing
ISBN
0387985425 (acid-free paper)
서지주기
Includes bibliographical references (p. 203-212) and indexes.
일반주제명
Algebras, Linear. Linear models (Statistics)
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010 ▼a 98003959
020 ▼a 0387985425 (acid-free paper)
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
050 0 0 ▼a QA184 ▼b .G45 1998
082 0 0 ▼a 512/.5 ▼2 22
084 ▼a 512.5 ▼2 DDCK
090 ▼a 512.5 ▼b G338n
100 1 ▼a Gentle, James E., ▼d 1943-.
245 1 0 ▼a Numerical linear algebra for applications in statistics / ▼c James E. Gentle.
260 ▼a New York : ▼b Springer, ▼c c1998.
300 ▼a xiii, 221 p. : ▼b ill. ; ▼c 24 cm.
490 1 ▼a Statistics and computing
504 ▼a Includes bibliographical references (p. 203-212) and indexes.
650 0 ▼a Algebras, Linear.
650 0 ▼a Linear models (Statistics)
830 0 ▼a Statistics and computing.
945 ▼a KLPA

소장정보

No. 소장처 청구기호 등록번호 도서상태 반납예정일 예약 서비스
No. 1 소장처 과학도서관/Sci-Info(2층서고)/ 청구기호 512.5 G338n 등록번호 121198307 도서상태 대출가능 반납예정일 예약 서비스 B M

컨텐츠정보

목차

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.- 2.1.1 Operations on Vectors; Vector Spaces.- 2.1.2 Vectors and Matrices.- 2.1.3 Operations on Vectors and Matrices.- 2.1.4 Partitioned Matrices.- 2.1.5 Matrix Rank.- 2.1.6 Identity Matrices.- 2.1.7 Inverses.- 2.1.8 Linear Systems.- 2.1.9 Generalized Inverses.- 2.1.10 Other Special Vectors and Matrices.- 2.1.11 Eigenanalysis.- 2.1.12 Similarity Transformations.- 2.1.13 Norms.- 2.1.14 Matrix Norms.- 2.1.15 Orthogonal Transformations.- 2.1.16 Orthogonalization Transformations.- 2.1.17 Condition of Matrices.- 2.1.18 Matrix Derivatives.- 2.2 Computer Representations and Basic Operations.- 2.2.1 Computer Representation of Vectors and Matrices.- 2.2.2 Multiplication of Vectors and Matrices.- Exercises.- 3 Solution of Linear Systems.- 3.1 Gaussian Elimination.- 3.2 Matrix Factorizations.- 3.2.1 LU and LDU Factorizations.- 3.2.2 Cholesky Factorization.- 3.2.3 QR Factorization.- 3.2.4 Householder Transformations (Reflections).- 3.2.5 Givens Transformations (Rotations).- 3.2.6 Gram-Schmidt Transformations.- 3.2.7 Singular Value Factorization.- 3.2.8 Choice of Direct Methods.- 3.3 Iterative Methods.- 3.3.1 The Gauss-Seidel Method with Successive Overrelaxation.- 3.3.2 Solution of Linear Systems as an Optimization Problem; Conjugate Gradient Methods.- 3.4 Numerical Accuracy.- 3.5 Iterative Refinement.- 3.6 Updating a Solution.- 3.7 Overdetermined Systems; Least Squares.- 3.7.1 Full Rank Coefficient Matrix.- 3.7.2 Coefficient Matrix Not of Full Rank.- 3.7.3 Updating a Solution to an Overdetermined System.- 3.8 Other Computations for Linear Systems.- 3.8.1 Rank Determination.- 3.8.2 Computing the Determinant.- 3.8.3 Computing the Condition Number.- 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.- 5.1.1 BLAS.- 5.1.2 Fortran and C Libraries.- 5.1.3 Fortran 90 and 95.- 5.2 Interactive Systems for Array Manipulation.- 5.2.1 Matlab.- 5.2.2 S, S-Plus.- 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.- 6.2.1 The Normal Equations and the Sweep Operator.- 6.2.2 Linear Least Squares Subject to Linear Equality Constraints.- 6.2.3 Weighted Least Squares.- 6.2.4 Updating Linear Regression Statistics.- 6.2.5 Tests of Hypotheses.- 6.2.6 D-Optimal Designs.- 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.


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