作者︰(美國)龐濤 (Tao Pang)
preface to first editionprefaceacknowledgments1 introduction 1.1 computation and science 1.2 the emergence of modem computers 1.3 computer algorithms and languages exercises2 approximation of a function 2.1 interpolation 2.2 least-squares approximation 2.3 the millikan experiment 2.4 spline approximation 2.5 random-number generators exercises3 numerical calculus 3.1 numerical differentiation 3.2 numerical integration 3.3 roots of an equation 3.4 extremes of a function 3.5 classical scattering exercises4 ordinary differential equations 4.1 initial-value problems 4.2 the euler and picard methods 4.3 predictor-corrector methods 4.4 the runge-kutta method 4.5 chaotic dynamics of a driven pendulum 4.6 boundary-value and eigenvalue problems 4.7 the shooting method 4.8 linear equations and the sturm-liouville problem 4.9 the one-dimensional schr6dinger equation exercises5 numerical methods for matrices 5.1 matrices in physics 5.2 basic matrix operations 5.3 linear equation systems 5.4 zeros and extremes of multivariable functions 5.5 eigenvalue problems 5.6 the faddeev-leverrier method 5.7 complex zeros of a polynomial 5.8 electronic structures of atoms 5.9 the lanczos algorithm and the many-body problem 5.10 random matrices exercises6 spectral analysis 6.1 fourier analysis and orthogonal functions 6.2 discrete fourier transform 6.3 fast fourier transform 6.4 power spectrum of a driven pendulum 6.5 fourier transform in higher dimensions 6.6 wavelet analysis 6.7 discrete wavelet transform 6.8 special functions 6.9 gaussian quadratures exercises7 partial differential equations 7.1 partial differential equations in physics 7.2 separation of variables 7.3 discretization of the equation 7.4 the matrix method for difference equations 7.5 the relaxation method 7.6 groundwater dynamics 7.7 initial-value problems 7.8 temperature field of a nuclear waste rod exercises8 molecular dynamics simulations 8.1 general behavior of a classical system 8.2 basic methods for many-body systems 8.3 the verlet algorithm 8.4 structure of atomic clusters 8.5 the gear predictor-corrector method 8.6 constant pressure, temperature, and bond length 8.7 structure and dynamics of real materials 8.8 ab initio molecular dynamics exercises9 modeling continuous systems 9.1 hydrodynamic equations 9.2 the basic finite element method 9.3 the ritz variational method 9.4 higher-dimensional systems 9.5 the finite element method for nonlinear equations 9.6 the particle-in-cell method 9.7 hydrodynamics and magnetohydrodynamics 9.8 the lattice boltzmann method exercises10 monte carlo simulations 10.1 sampling and integration 10.2 the metropolis algorithm 10.3 applications in statistical physics 10.4 critical slowing down and block algorithms 10.5 variational quantum monte carlo simulations 10.6 green's function monte carlo simulations 10.7 two-dimensional electron gas 10.8 path-integral monte carlo simulations 10.9 quantum lattice models exercises11 genetic algorithm and programming 11.1 basic elements of a genetic algorithm 11.2 the thomson problem 11.3 continuous genetic algorithm 11.4 other applications 11.5 genetic programming exercises12 numerical renormalization 12.1 the scaling concept 12.2 renormalization transform 12.3 critical phenomena: the ising model 12.4 renormalization with monte carlo simulation 12.5 crossover: the kondo problem 12.6 quantum lattice renormalization 12.7 density matrix renormalization exercisesreferencesindex
版權頁︰插圖︰The basic idea behind a genetic algorithm is to follow the biological processof evolution in selecting the path to reach an optimal configuration of a givencomplex system. For exampie, for an interacting many-body system, the equilib-rium is reached by moving the system to the configuration that is at the globalminimum on its potential energy surface. This is single-objective optimization,which can be described mathematically as searching for the global minimum ofa multivariable function. Multiobjective optimization involvesmore than one equation, for example, a search for the minima of gk Both types ofoptimization can involve some constraints.We limit ourselves to single-objective optimization here. For a detailed dis-cussion on multi-objective optimization using the genetic algorithm, see Deb.
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