计算数学及力学随机变量的适应性方法ADAPTIVE METHODS OF COMPUTING MATHEMATICS

Foreword
Part I. Evaluation of integrals and solution of integral equations
Chapter 1. Fundamentals of the Monte-Carlo method
1.1. Idea of the Monte-Carlo method
1.2. Simulation of implementation of a scalarrandom variable
1.2.1. The transforming functions method
1.2.2. The superposition method
1.2.3. The selection method
1.3. Simulation of implementation of a vector
random variable
1.4. Evaluation of definite integrals
by means of Monte-Carlo method
Chapter 2. Evaluation of integrals by means of statistic
simulation employing adaptation
2.1. Adaptation idea in statistic methods of numerical analysis, based on the principles of importance sampling
2.2. Adaptive algorithm for evaluating
one-dimensional integral
2.2.1. Selection of probability densities
2.2.2. Evaluation procedure
2.2.3. Results of numerical experiments
2.2.4. Report on the results
2.3. Adaptive algorithm of evaluation of two-dimensional
and multi-dimensional integrals
2.3.1. Description of the algorithm
2.3.2. Results of numerical experiments
2.3.3. Some comments
2.4. Stochastic computing algorithms as an object of adaptive control
2.4.1. Introduction
2.4.2. Statement of a problem of control over the process of computation
2.4.3. Synthesis of the optimal control over the process of computation
2.4.4. Strategy of adaptive optimization of computation process
Chapter 3. Semi-statistical method of numerical solving integral equations
3.1. Introduction
3.2. Basic relations of the method
3.3. Recurrent inversion formulae
3.4. Convergence of the method
3.5. Adaptive abilities of the algorithm
3.6. Qualitative considerations concerning connections between the semi-statistical and variational methods
3.7. Application of the method to singular integral equations
3.7.1. Description and application of the method
3.7.2. Recurrent inversion formulae
3.7.3. Analysis of the method's errors
3.7.4. Adaptive abilities of the algorithm
Chapter 4. Projection-statistical method of numerical solution of integral equations
4.1. Introduction
4.2. Basic relations of the method
4.3. Formulae of recurrent inversion
4.4. The algorithm convergence
4.5. Merits of the method
4.6. Adaptive abilities
4.7. Peculiarities of numerical implementation
4.8. An alternative computing technique: approximate solutions should be averaged
4.9. Numerical experiments
……
PartII.The random walk metbod.Solution of boundary-value problems
PartIII.Optimization of an FEM grid
Afterword
Bibliograhy
Index