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1.

図書

図書
Werner C. Rheinboldt
出版情報: Philadelphia : Society for Industrial and Applied Mathematics, c1998  ix, 148 p. ; 26 cm
シリーズ名: CBMS-NSF regional conference series in applied mathematics ; 70
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Preface to the Second Edition
Preface to the First Edition
Introduction / Chapter 1.:
Problem Overview / 1.1:
Notation and Background / 1.2:
Model Problems / Chapter 2.:
Discretization of Operator Equations / 2.1:
Minimization / 2.2:
Discrete Problems / 2.3:
Iterative Processes and Rates of Convergence / Chapter 3.:
Characterization of Iterative Processes / 3.1:
Rates of Convergence / 3.2:
Evaluation of Convergence Rates / 3.3:
On Efficiency and Accuracy / 3.4:
Methods of Newton Type / Chapter 4.:
The Linearization Concept / 4.1:
Methods of Newton Form / 4.2:
Discretized Newton Methods / 4.3:
Attraction Basins / 4.4:
Methods of Secant Type / Chapter 5.:
General Secant Methods / 5.1:
Consistent Approximations / 5.2:
Update Methods / 5.3:
Combinations of Processes / Chapter 6.:
The Use of Classical Linear Methods / 6.1:
Nonlinear SOR Methods / 6.2:
Residual Convergence Controls / 6.3:
Inexact Newton Methods / 6.4:
Parametrized Systems of Equations / Chapter 7.:
Submanifolds of R[superscript n] / 7.1:
Continuation Using ODEs / 7.2:
Continuation with Local Parametrizations / 7.3:
Simplicial Approximations of Manifolds / 7.4:
Unconstrained Minimization Methods / Chapter 8.:
Admissible Step-Length Algorithms / 8.1:
Gradient-Related Methods / 8.2:
Collectively Gradient-Related Directions / 8.3:
Trust Region Methods / 8.4:
Nonlinear Generalizations of Several Matrix Classes / Chapter 9.:
Basic Function Classes / 9.1:
Properties of the Function Classes / 9.2:
Convergence of Iterative Processes / 9.3:
Outlook at Further Methods / Chapter 10.:
Higher-Order Methods / 10.1:
Piecewise-Linear Methods / 10.2:
Further Minimization Methods / 10.3:
Bibliography
Index
Preface to the Second Edition
Preface to the First Edition
Introduction / Chapter 1.:
2.

図書

図書
William H. Press ... [et al.]
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1996  xxxi, 933 p.: ill. ; 25 cm
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Legal matters
List of computer programs
Preliminaries / 1:
Solution of linear algebraic equations / 2:
Interpolation and extrapolation / 3:
Integration of functions / 4:
Evaluation of functions / 5:
Special functions / 6:
Random numbers / 7:
Sorting / 8:
Root finding and nonlinear sets of equations / 9:
Minimization or maximization of functions / 10:
Eigensystems / 11:
Fast Fourier transform / 12:
Fourier and spectral applications / 13:
Statistical description of data / 14:
Modeling of data / 15:
Integration of ordinary differential equations / 16:
Two point boundary value problems / 17:
Integral equations and inverse theory / 18:
Partial differential equations / 19:
Less-numerical algorithms / 20:
References
Index of programs and dependencies
General index
Legal matters
List of computer programs
Preliminaries / 1:
3.

図書

図書
William H. Press ... [et al.]
出版情報: Cambridge [England] ; New York : Cambridge University Press, 1996  xx p., p. 935-1486 ; 25 cm
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Introduction to Fortran 90 language features / 1:
Introduction to parallel programming / 2:
Numerical recipes utility functions for Fortran 90 / 3:
Fortran 90 Code chapters / Part I:
Preliminaries / 4:
Solution of linear algebraic equations / 5:
Interpolation and extrapolation / 6:
Integration of functions / 7:
Evaluation of functions / 8:
Special functions / 9:
Random numbers / 10:
Sorting / 11:
Root finding and nonlinear sets of equations / 12:
Minimization or maximization of functions / 13:
Eigensystems / 14:
Fast Fourier transform / 15:
Fourier and spectral applications / 16:
Statistical description of Data / 17:
Modelling of data / 18:
Integration of ordinary differential equations / 19:
Two point boundary value problems / 20:
Integral equations and inverse theory / 21:
Partial differential equations / 22:
Less-numerical algorithms / 23:
Appendices / Part II:
Listing of utility modules (nrtype and nrutil) / 24:
Listing of explicit interfaces / 25:
Index of programs and dependencies / 26:
Introduction to Fortran 90 language features / 1:
Introduction to parallel programming / 2:
Numerical recipes utility functions for Fortran 90 / 3:
4.

図書

図書
Nicholas J. Higham
出版情報: Philadelphia : Society for Industrial and Applied Mathematics, c1996  xxviii, 688 p. ; 24 cm
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List of Figures
List of Tables
Preface to Second Edition
Preface to First Edition
About the Dedication
Principles of Finite Precision Computation / 1:
Notation and Background / 1.1:
Relative Error and Significant Digits / 1.2:
Sources of Errors / 1.3:
Precision Versus Accuracy / 1.4:
Backward and Forward Errors / 1.5:
Conditioning / 1.6:
Cancellation / 1.7:
Solving a Quadratic Equation / 1.8:
Computing the Sample Variance / 1.9:
Solving Linear Equations / 1.10:
Accumulation of Rounding Errors / 1.11:
Instability Without Cancellation / 1.12:
Increasing the Precision / 1.13:
Cancellation of Rounding Errors / 1.14:
Rounding Errors Can Be Beneficial / 1.15:
Stability of an Algorithm Depends on the Problem / 1.16:
Rounding Errors Are Not Random / 1.17:
Designing Stable Algorithms / 1.18:
Misconceptions / 1.19:
Rounding Errors in Numerical Analysis / 1.20:
Notes and References / 1.21:
Problems
Floating Point Arithmetic / 2:
Floating Point Number System / 2.1:
Model of Arithmetic / 2.2:
IEEE Arithmetic / 2.3:
Aberrant Arithmetics / 2.4:
Exact Subtraction / 2.5:
Fused Multiply-Add Operation / 2.6:
Choice of Base and Distribution of Numbers / 2.7:
Statistical Distribution of Rounding Errors / 2.8:
Alternative Number Systems / 2.9:
Elementary Functions / 2.10:
Accuracy Tests / 2.11:
Basics / 2.12:
Inner and Outer Products / 3.1:
The Purpose of Rounding Error Analysis / 3.2:
Running Error Analysis / 3.3:
Notation for Error Analysis / 3.4:
Matrix Multiplication / 3.5:
Complex Arithmetic / 3.6:
Miscellany / 3.7:
Error Analysis Demystified / 3.8:
Other Approaches / 3.9:
Summation / 3.10:
Summation Methods / 4.1:
Error Analysis / 4.2:
Compensated Summation / 4.3:
Other Summation Methods / 4.4:
Statistical Estimates of Accuracy / 4.5:
Choice of Method / 4.6:
Polynomials / 4.7:
Horner's Method / 5.1:
Evaluating Derivatives / 5.2:
The Newton Form and Polynomial Interpolation / 5.3:
Matrix Polynomials / 5.4:
Norms / 5.5:
Vector Norms / 6.1:
Matrix Norms / 6.2:
The Matrix p-Norm / 6.3:
Singular Value Decomposition / 6.4:
Perturbation Theory for Linear Systems / 6.5:
Normwise Analysis / 7.1:
Componentwise Analysis / 7.2:
Scaling to Minimize the Condition Number / 7.3:
The Matrix Inverse / 7.4:
Extensions / 7.5:
Numerical Stability / 7.6:
Practical Error Bounds / 7.7:
Perturbation Theory by Calculus / 7.8:
Triangular Systems / 7.9:
Backward Error Analysis / 8.1:
Forward Error Analysis / 8.2:
Bounds for the Inverse / 8.3:
A Parallel Fan-In Algorithm / 8.4:
LU Factorization and Linear Equations / 8.5:
Gaussian Elimination and Pivoting Strategies / 9.1:
LU Factorization / 9.2:
The Growth Factor / 9.3:
Diagonally Dominant and Banded Matrices / 9.5:
Tridiagonal Matrices / 9.6:
More Error Bounds / 9.7:
Scaling and Choice of Pivoting Strategy / 9.8:
Variants of Gaussian Elimination / 9.9:
A Posteriori Stability Tests / 9.10:
Sensitivity of the LU Factorization / 9.11:
Rank-Revealing LU Factorizations / 9.12:
Historical Perspective / 9.13:
Cholesky Factorization / 9.14:
Symmetric Positive Definite Matrices / 10.1:
Sensitivity of the Cholesky Factorization / 10.2:
Positive Semidefinite Matrices / 10.3:
Matrices with Positive Definite Symmetric Part / 10.4:
Symmetric Indefinite and Skew-Symmetric Systems / 10.5:
Block LDL[superscript T] Factorization for Symmetric Matrices / 11.1:
Aasen's Method / 11.2:
Block LDL[superscript T] Factorization for Skew-Symmetric Matrices / 11.3:
Iterative Refinement / 11.4:
Behaviour of the Forward Error / 12.1:
Iterative Refinement Implies Stability / 12.2:
Block LU Factorization / 12.3:
Block Versus Partitioned LU Factorization / 13.1:
Error Analysis of Partitioned LU Factorization / 13.2:
Error Analysis of Block LU Factorization / 13.3:
Matrix Inversion / 13.4:
Use and Abuse of the Matrix Inverse / 14.1:
Inverting a Triangular Matrix / 14.2:
Inverting a Full Matrix by LU Factorization / 14.3:
Gauss-Jordan Elimination / 14.4:
Parallel Inversion Methods / 14.5:
The Determinant / 14.6:
Condition Number Estimation / 14.7:
How to Estimate Componentwise Condition Numbers / 15.1:
The p-Norm Power Method / 15.2:
LAPACK 1-Norm Estimator / 15.3:
Block 1-Norm Estimator / 15.4:
Other Condition Estimators / 15.5:
Condition Numbers of Tridiagonal Matrices / 15.6:
The Sylvester Equation / 15.7:
Solving the Sylvester Equation / 16.1:
Backward Error / 16.2:
Perturbation Result / 16.3:
Stationary Iterative Methods / 16.4:
Survey of Error Analysis / 17.1:
Singular Systems / 17.2:
Stopping an Iterative Method / 17.5:
Matrix Powers / 17.6:
Matrix Powers in Exact Arithmetic / 18.1:
Bounds for Finite Precision Arithmetic / 18.2:
Application to Stationary Iteration / 18.3:
QR Factorization / 18.4:
Householder Transformations / 19.1:
Error Analysis of Householder Computations / 19.2:
Pivoting and Row-Wise Stability / 19.4:
Aggregated Householder Transformations / 19.5:
Givens Rotations / 19.6:
Gram-Schmidt Orthogonalization / 19.7:
Sensitivity of the QR Factorization / 19.9:
The Least Squares Problem / 19.10:
Perturbation Theory / 20.1:
Solution by QR Factorization / 20.2:
Solution by the Modified Gram-Schmidt Method / 20.3:
The Normal Equations / 20.4:
The Seminormal Equations / 20.5:
Weighted Least Squares Problems / 20.7:
The Equality Constrained Least Squares Problem / 20.9:
Proof of Wedin's Theorem / 20.10:
Underdetermined Systems / 20.11:
Solution Methods / 21.1:
Perturbation Theory and Backward Error / 21.2:
Vandermonde Systems / 21.3:
Primal and Dual Systems / 22.1:
Stability / 22.3:
Fast Matrix Multiplication / 22.4:
Methods / 23.1:
The Fast Fourier Transform and Applications / 23.2:
The Fast Fourier Transform / 24.1:
Circulant Linear Systems / 24.2:
Nonlinear Systems and Newton's Method / 24.3:
Newton's Method / 25.1:
Special Cases and Experiments / 25.2:
Automatic Error Analysis / 25.4:
Exploiting Direct Search Optimization / 26.1:
Direct Search Methods / 26.2:
Examples of Direct Search / 26.3:
Interval Analysis / 26.4:
Other Work / 26.5:
Software Issues in Floating Point Arithmetic / 26.6:
Exploiting IEEE Arithmetic / 27.1:
Subtleties of Floating Point Arithmetic / 27.2:
Cray Peculiarities / 27.3:
Compilers / 27.4:
Determining Properties of Floating Point Arithmetic / 27.5:
Testing a Floating Point Arithmetic / 27.6:
Portability / 27.7:
Avoiding Underflow and Overflow / 27.8:
Multiple Precision Arithmetic / 27.9:
Extended and Mixed Precision BLAS / 27.10:
Patriot Missile Software Problem / 27.11:
A Gallery of Test Matrices / 27.12:
The Hilbert and Cauchy Matrices / 28.1:
Random Matrices / 28.2:
"Randsvd" Matrices / 28.3:
The Pascal Matrix / 28.4:
Tridiagonal Toeplitz Matrices / 28.5:
Companion Matrices / 28.6:
Solutions to Problems / 28.7:
Acquiring Software / B:
Internet / B.1:
Netlib / B.2:
MATLAB / B.3:
NAG Library and NAGWare F95 Compiler / B.4:
Program Libraries / C:
Basic Linear Algebra Subprograms / C.1:
EISPACK / C.2:
LINPACK / C.3:
LAPACK / C.4:
The Matrix Computation Toolbox / D:
Bibliography
List of Figures
List of Tables
Preface to Second Edition
5.

図書

図書
Lydia Kronsjö
出版情報: Chichester ; New York : Wiley, c1987  xiii, 363 p. ; 24 cm
シリーズ名: Wiley series in computing
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6.

図書

図書
U. Schendel ; translator, B.W. Conolly
出版情報: Chichester : E. Horwood , New York : Halsted Press, c1984  151 p. ; 24 cm
シリーズ名: Ellis Horwood series in mathematics and its applications ; . Statistics and operational research
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7.

図書

図書
Jaroslav Pachner
出版情報: New York : McGraw-Hill, c1984  1 v. (various pagings) ; 25 cm
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8.

図書

図書
Arthur P. Boresi and Ken P. Chong
出版情報: London ; New York : Elsevier Applied Science, c1991  viii, 147 p. ; 23 cm
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9.

図書

図書
Richard E. Crandall
出版情報: Santa Clara, Calif. : TELOS, c1994  xxiv, 470 p. ; 25 cm.
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10.

図書

図書
J.C. Nash
出版情報: Bristol : Hilger, 1979  ix,227p ; 26cm
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