Preface Notation 1 Scientific Computing 1.1 Introduction 1.2 Approximations in Scientific Computation 1.3 Computer Arithmetic 1.4 Mathematical Software 1.5 Historical Notes and Further Reading
2 Systems of Linear Equations 2.1 Linear Systems 2.2 Existence and Uniqueness 2.3 Sensitivity and Conditioning 2.4 Solving Linear Systems 2.5 Special Types of Linear Systems 2.6 Iterative Methods for Linear Systems 2.7 Software for Linear Systems 2.8 Historical Notes and Further Reading
3 Linear Least Squares 3.1 Linear Least Squares Problems 3.2 Existence and Uniqueness 3.3 Sensitivity and Conditioning 3.4 Problem Transformations 3.5 Orthogonalization Methods 3.6 Singular Value Decomposition 3.7 Comparison of Methods 3.8 Software for Linear Least Squares 3.9 Historical Notes and Further Reading
4 Eigenvalue Problems 4.1 Eigenvalues and Eigenvectors 4.2 Existence and Uniqueness 4.3 Sensitivity and Conditioning 4.4 Problem Transformations 4.5 Computing Eigenvalues and Eigenvectors 4.6 Generalized Eigenvalue Problems 4.7 Computing the Singular Value Decomposition 4.8 Software for Eigenvalue Problems 4.9 Historical Notes and Further Reading
5 Nonlinear Equations 5.1 Nonlinear Equations 5.2 Existence and Uniqueness 5.3 Sensitivity and Conditioning 5.4 Convergence Rates and Stopping Criteria 5.5 Nonlinear Equations in One Dimension 5.6 Systems of Nonlinear Equations 5.7 Software for Nonlinear Equations 5.8 Historical Notes and Farther Reading
6 Optimization 6.1 Optimization Problems 6.2 Existence and Uniqueness 6.3 Sensitivity and Conditioning 6.4 Optimization in One Dimension 6.5 Unconstrained Optimization 6.6 Nonlinear Least Squares 6.7 Constrained Optimization 6.8 Software for Optimization 6.9 Historical Notes and Further Reading
7 Interpolation 7.1 Interpolation 7.2 Existence, Uniqueness, and Conditioning 7.3 Polynomial Interpolation 7.4 Piecewise Polynomial Interpolation 7.5 Software for Interpolation 7.6 Historical Notes and Further Reading
8 Numerical Integration and Differentiation 8.1 Integration 8.2 Existence, Uniqueness, and Conditioning 8.3 Numerical Quadrature 8.4 Other Integration Problems 8.5 Integral Equations 8.6 Numerical Differentiation 8.7 Richardson Extrapolation 8.8 Software for Integration and Differentiation 8.9 Historical Notes and Further Reading
9 Initial Value Problems for ODEs 9.1 Ordinary Differential Equations 9.2 Existence, Uniqueness, and Conditioning 9.3 Numerical Solution of ODES 9.4 Software for ODE Initial Value Problems 9.8 Historical Notes and Further Reading
10 Boundary Value Problems for ODEs 10.1 Boundary Value Problems 10.2 Existence, Uniqueness, and Conditioning 10.3 Shooting Method 10.4 Finite Difference Method 10.5 Collocation Method 10.6 Galerkin Method 10.7 Eigenvalue Problems 10.8 Software for ODE Boundary Value Problems 10.9 Historical Notes and Further Reading
11 Partial Differential Equations 11.1 Partial Differential Equations 11.2 Time-Dependent Problems 11.3 Time-Independent Problems 11.4 Direct Methods for Sparse Linear Systems 11.5 Iterative Methods for Linear Systems 11.6 Comparison of Methods 11.7 Software for Partial Differential Equations 11.8 Historical Notes and Further Reading
12 Fast Fourier Transform 12.1 Trigonometric Interpolation 12.2 FFT Algorithm 12.3 Applications of DFT 12.4 Wavelets 12.5 Software for FFT 12.6 Historical Notes and Further Reading
13 Random Numbers and Simulation 13.1 Stochastic Simulation 13.2 Randomness and Random Numbers 13.3 Random Number Generators 13.4 Quasi-Random Sequences 13.5 Software for Generating Random Numbers 13.6 Historical Notes and Further Reading
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