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| Numerical Computation Motivation and Objectives | |
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| Number Representation | |
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| Machine Precision | |
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| Round-Off Error | |
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| Truncation Error | |
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| Random Number Generation | |
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| Numerical Software | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Linear Algebraic Systems Motivation and Objectives | |
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| Gauss-Jordan Elimination | |
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| Gaussian Elimination | |
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| LU Decomposition | |
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| Ill-Conditioned Systems | |
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| Iterative Methods | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Eigenvalues and Eigenvectors Motivation and Objectives | |
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| The Characteristic Polynomial | |
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| Power Methods | |
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| Jacobi''s Method | |
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| Householder Transformation | |
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| QR Method | |
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| Danilevsky''s Method | |
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| Polynomial Roots | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Curve Fitting Motivation and Objectives | |
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| Interpolation | |
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| Newton''s Difference Formula | |
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| Cubic Splines | |
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| Least Square | |
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| Two-Dimensional Interpolation | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Root Finding Motivation and Objectives | |
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| Bracketing Methods | |
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| Contraction Mapping Method | |
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| Secant Method | |
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| Muller''s Method | |
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| Newton''s Method | |
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| Polynomial Roots | |
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| Nonlinear Systems of Equations | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Optimization Motivation and Objectives | |
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| Local and Global Minima | |
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| Line Searches | |
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| Steepest Descent Method | |
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| Conjugate-Gradient Method | |
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| Quasi-Newton Methods | |
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| Penalty Functions | |
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| Simulated Annealing | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Differentiation and Integration Motivation and Objectives | |
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| Numerical Differentiation | |
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| Noise-Corrupted Data | |
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| Newton-Cotes Integration Formulas | |
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| Romberg Integration | |
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| Gauss Quadrature | |
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| Improper Integrals | |
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| Multiple Integrals | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Ordinary Differential Equations Motivation and Objectives | |
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| Euler''s Method | |
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| Runge-Kutta Methods | |
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| Step Size Control | |
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| Multi-Step Methods | |
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| Bulirsch-Stoer Extrapolation Methods | |
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| Stiff Differential Equations | |
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| Boundary Value Problems | |
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| Applications | |
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| Summary | |
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| Problems | |
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| Partial Differential Equations Motivation and Objectives | |
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| Elliptic Equations | |
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| One-Dimensional Parabolic Equations | |
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| Two-Dimensional Parabolic Equations | |
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| One-Dimensional Hyperbolic Equations | |
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| Two-Dimensional Hyperbolic Equations | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| Digital Signal Processing Motivation and Objectives | |
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| Fourier Transform | |
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| Fast Fourier Transform (FFT) | |
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| Correlation | |
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| Convolution Digital Filters | |
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| Two-Dimensional FFT | |
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| System Identification | |
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| Applications | |
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| Chapter Summary | |
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| Problems | |
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| References And Further Reading | |
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| Nlib Using Matlab? | |
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| A Numerical Toolbox: NLIB | |
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| Main-Program Support | |
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| Linear Algebraic Systems | |
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| Eigenvalues and Eigenvectors | |
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| Curve Fitting | |
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| Root Finding | |
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| Optimization | |
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| Differentiation and Integration | |
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| Ordinary Differential Equations | |
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| Partial Differential Equations | |
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| Digital Signal Processing | |
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| Nlib Using C | |
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| A Numerical Library: NLIB | |
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| NLIB Data Types | |
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| NLIB Core: nlib.c | |
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| Tabular Display: show.c | |
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| Graphical Display: draw.c | |
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| Linear Algebraic Systems: linear.c | |
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| Eigenvalues and Eigenvectors: eigen.c | |
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| Curve Fitting: curves.c | |
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| Root Finding: roots.c | |
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| Optimization: optim.c | |
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| Differentiation and Integration: integ.c | |
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| Ordinary Differential Equations: ode.c | |
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| Partial Differential Equations: pde.c | |
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| Digital Signal Processing: dsp.c | |
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| Vectors and Matrices | |
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| Vector and Matrix Notation | |
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| Basic Operations | |
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| Inverses | |
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| Eigenvalues and Eigenvectors | |
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| Vector Norms | |
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| Answers to Selected Problems | |
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| Index | |