音像计算物理学(第2版)(英文版)(德)P.J.谢勒(Philipp J.S

Part I Numerical Methods
1 Error Analysis
1.1 Machine Numbers and Rounding Errors
1.2 Numerical Errors of Elementary Floating Point Oraios
1.2.1 Numerical Extinction
1.2.2 Addition
1.. Multiplication
1.3 Error Propagation
1.4 Stability of lterative Algorithms
1.5 Example: Rotation
1.6 Truncation Error
1.7 Problems
2 Interpolation
2.1 Interpolating Functions
2.2 Polynomial Interpolation
2.2.1 lagrange Polynomials
2.2.2 Barycentric Lagrange Interpolation
2.. Newton's Divided Differences
2.2.4 Neville Method
2.2.5 Error of Polynomial Interpolation
. Splice Interpolation
2.4 Rational Interpolation
2.4.1 Pad6 Approximant
2.4.2 Barycentric Rational Interpolation
2.5 Multivariate Interpolation
2.6 Problems
3 Numerical Differentiation
3.1 One-Sided Difference otient
3.2 Central Difference otient
3.3 Extrapolation Methods
3.4 Higher Derivatives
3.5 Partial Derivatives of Multivariate Functions
3.6 Problems
4 Numerical Integration
4.1 Equidistant Sample Points
4.1.1 Closed Newton-Cotes Formulae
4.1.2 Open Newton-Cotes Formulae
4.1.3 Coite Newton-Cotes Rules
4.1.4 Extrapolation Method (Romberg Integration)
4.2 Optimized Sample Points
4.2.1 Clenshaw-Curtis Expressions
4.2.2 Gaussian Integration.
4.3 Problems
5 Systems of Inhomogeneous Linear Equations
5.1 Gaussian Elimination Method
5.1.1 Pivoting
5.1.2 Direct LU Decoition
5.2 R Decoition
5.2.1 R Decoition by Orthogonalization
5.2.2 R Decoition by Householder Reflections
5.3 Linear Equations with Tridiagonal Matrix
5.4 Cyclic Tridiagonal Systems
5.5 Iterative Solution of Inhomogeneous Linear Equations
5.5.1 General Relaxation Method
5.5.2 Jacobi Method
5.5.3 Gauss-Seidel Method
5.5.4 Damping and Successive Over-Relaxation
5.6 Conjugate Gradients
5.7 Matrix Inversion
5.8 Problems
6 Roots and Extremai Points
6.1 Root Finding
6.1.1 Bisection
6.1.2 Regula Falsi (False Position) Method
6.1.3 Newton-Raphson Method
6.1.4 Secant Method
6.1.5 Interpolation
6.1.6 Inverse Interpolation
6.1.7 Combined Methods
6.1.8 Multidimensional Root Finding
6.1.9 si-Newton Methods
6.2 Function Minimization
6.2.1 The Ternary Search MetlTod
6.2.2 The Golden Section Search Method (Brent's Method)
6.. Minimization in Multidimensions
6.2.4 Steepest Descent Method
6.2.5 Conjugate Gradient Method
6.2.6 Newton-R~phson Method
6.2.7 si-Newton Methods
6.3 Problems
7 Fourier Transformation
8 Random Numbers and Monte Carlo Methods
9 Eigenvalue Problems
10 Data Fitting
11 Discretization of Differential Equations
12 Equations of Motion
Part II Simulation of Classical and ntum Systems
13 Rotational Motion
14 Molecular Mechanics
15 Thermodynamic Systems
16 Random Walk and Brownian Motion
17 Electrostatics
18 Waves
19 Diffusion
20 Nonlinear Systems
21 Simple ntum Systems
Appendix I Performing the Computer Experiments
Appendix II Methods and Algorithms
References
Index