Minimax Models in the Theory of Numerical Methods
In the Russian edition published in 1989, this book was called "Minimax Algorithms in Problems of Numerical Analysis". The new title is better related to the subject of the book and its style. The basis for every decision or inference concerning the ways to solve a given problem is the com...
| Main Author: | |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1992, 1992
|
| Edition: | 1st ed. 1992 |
| Series: | Theory and Decision Library B, Mathematical and Statistical Methods
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- 1. General Computation Model
- 1. Basic concepts
- 2. Functional classes under consideration
- 3. Classes of deterministic algorithms
- 4. Minimax concept of optimality and specific notions of optimality
- 5. Comparison of the best guaranteed results for adaptive and nonadaptive algorithms
- 6. Sequentially optimal algorithms
- 7. Stochastic algorithms
- 2. Numerical Integration
- 1. Optimal quadratures for functional classes determined by quasi-metrics
- 2. Optimal quadratures for functional classes determined by moduli of continuity
- 3. Sequentially optimal and one-step optimal integration algorithms
- 4. Numerical tests
- 5. Optimal computation of iterated integrals
- 6. Computation of multiple integrals using Peano type developments
- 3. Recovery of Functions from Their Values
- 1. Optimal nonadaptive algorithms
- 2. Sequentially optimal and one-step optimal recovery algorithms
- 3. Solution of a multistep antagonistic game related to the problem of optimal recovery
- 4. Search for the Global Extremum
- 1. On the choice of starting points for local optimization methods
- 2. Optimal nonadaptive search for a functional class determined by a quasi-metric
- 3. Reduction of the problem of constructing a sequentially optimal algorithm for a functional dass determined by a quasi-metric to aseries of problems of optimal covering
- 4. Specific computational algorithms
- 5. Case of approximate information
- 6. One-step optimal stochastic algorithm
- 5. Some Special Classes of Extremal Problems
- 1. Solution of equations and systems of equations
- 2. Maximization of a minimum function with coupled variables
- 3. Optimization with several criteria
- Author Index