C++ Scientific Programming : Computational Recipes at a Higher Level

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C++ Scientific Programming : Computational Recipes at a Higher Level

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  • 製本 Hardcover:ハードカバー版/ページ数 245 p.
  • 言語 ENG
  • 商品コード 9780471412106
  • DDC分類 005.133

Full Description


* Teaches the design of programs for scientific computation in C++* Introduces unique C++ classes, defines the particular relationships among these classes, and demonstrates their use in a dozen of the most powerful current applications* Presents a set of practices that allows programmers to embrace the attractive features of C++ without incurring undesired side effects and hidden costs Includes a collection of source code files downloadable from the Wiley ftp site Originally announced as Scientific Program Design: C++ for Native Fortran Writers

Table of Contents

Preface                                            xi
Overview 1 (11)
Classes and Operators 2 (4)
Memory Dynamics 6 (2)
Applications 8 (3)
Summary and Conclusions 11 (1)
Vector and Matrix Basics 12 (17)
Vector Class 12 (7)
Matrix Class 19 (7)
Miscellaneous Observations 26 (1)
Summary and Conclusions 27 (2)
Sparse Matrix Basics 29 (13)
Structure Definition 29 (1)
Class Definition 30 (11)
Summary and Conclusions 41 (1)
Conjugate-Gradient Methods 42 (12)
Linear Independence and Orthogonality 42 (2)
Steepest Descent 44 (1)
Conjugate Gradient 45 (3)
Extension to General Matrices 48 (1)
Biconjugate Gradient 49 (2)
Least Squares 51 (2)
Summary and Conclusions 53 (1)
Triangular Matrices 54 (15)
Backward Solvers 55 (2)
Forward Solvers 57 (2)
Spline Interpolation 59 (6)
Row and Column Permutations 65 (3)
Summary and Conclusions 68 (1)
Householder Matrix Methods 69 (18)
QR Factorization 71 (3)
Rank Deficiency 74 (2)
Least-Squares Applications 76 (4)
Eigenstuff 80 (2)
Givens Transformation 82 (3)
Summary and Conclusions 85 (2)
Singular Value Decomposition 87 (20)
Jacobi Transformation 87 (6)
The Pseudoinverse 93 (5)
Application to Two-Dimensional Images 98 (2)
Indirect SVD Methods 100(4)
Lanczos Method 104(1)
Summary and Conclusions 105(2)
Cholesky Decomposition 107(16)
Positive Definiteness and Pivoting 112(4)
Cholesky Solutions 116(1)
Quasidefinite Matrices 117(4)
Summary and Conclusions 121(2)
Automatic Derivatives 123(20)
Pointers to Functions 123(3)
Abstract Base Class 126(2)
The Chain Rule 128(2)
Constants and Variables 130(3)
C1 Functions 133(1)
Functions of Functions 134(3)
Multidimensional Applications 137(4)
Summary and Conclusions 141(2)
Constrained Optimization 143(18)
Linear Constraints 143(2)
Linear Objective Function 145(1)
Duality and Complementarity 146(2)
Interior-Point Method 148(4)
Solving LP Problems 152(2)
LP Applications 154(5)
Theoretical Addendum 159(1)
Summary and Conclusions 159(2)
Interior-Point Extensions 161(19)
L1 Regression as a Linear Programming 161(2)
Problem
L∞ Regression 163(4)
Quadratic Programming 167(4)
Successive Quadratic Programming 171(7)
Summary and Conclusions 178(2)
LU Factorization 180(18)
Crout LU Algorithm 180(2)
Dense Matrix Crout LU Subroutine 182(2)
Sparse Matrix Crout Subroutine 184(2)
Gauss LU Algorithm 186(3)
Threshold Pivoting 189(3)
Gauss LU Subroutine with Threshold Pivoting 192(2)
Comparison and Contrast 194(3)
Summary and Conclusions 197(1)
Complex Arrays 198(21)
Complex Array Templates 200(3)
Specialization 203(4)
Vector Sums and Differences 207(3)
Complex Matrices 210(3)
Quaternions 213(4)
Summary and Conclusions 217(2)
Fourier Transforms 219(20)
Bit Reversal 222(2)
FFT Implementations 224(4)
Connecting with the Real World 228(3)
FFT Member Functions 231(3)
Time and Space 234(3)
Summary and Conclusions 237(2)
References 239(2)
Index 241