Part III. NUMERICAL METHODS

Table of Contents

9. Competitive Analysis
9.1. 9.1 Notions, definitions
9.2. 9.2 The -server problem
9.3. 9.3 Models related to computer networks
9.3.1. 9.3.1 The data acknowledgement problem
9.3.2. 9.3.2 The file caching problem
9.3.3. 9.3.3 On-line routing
9.4. 9.4 On-line bin packing models
9.4.1. 9.4.1 On-line bin packing
9.4.2. 9.4.2 Multidimensional models
9.5. 9.5 On-line scheduling
9.5.1. 9.5.1 On-line scheduling models
9.5.2. 9.5.2 LIST model
9.5.3. 9.5.3 TIME model
10. Game Theory
10.1. 10.1 Finite games
10.1.1. 10.1.1 Enumeration
10.1.2. 10.1.2 Games represented by finite trees
10.2. 10.2 Continuous games
10.2.1. 10.2.1 Fixed-point methods based on best responses
10.2.2. 10.2.2 Applying Fan's inequality
10.2.3. 10.2.3 Solving the Kuhn-Tucker conditions
10.2.4. 10.2.4 Reduction to optimization problems
10.2.5. 10.2.5 Method of fictitious play
10.2.6. 10.2.6 Symmetric matrix games
10.2.7. 10.2.7 Linear programming and matrix games
10.2.8. 10.2.8 The method of von Neumann
10.2.9. 10.2.9 Diagonally strictly concave games
10.3. 10.3 The oligopoly problem
11. Recurrences
11.1. 11.1 Linear recurrence equations
11.1.1. 11.1.1 Linear homogeneous equations with constant coefficients
11.1.2. 11.1.2 Linear nonhomogeneous recurrence equations
11.2. 11.2 Generating functions and recurrence equations
11.2.1. 11.2.1 Definition and operations
11.2.2. 11.2.2 Solving recurrence equations by generating functions
11.2.3. 11.2.3 The Z-transform method
11.3. 11.3 Numerical solution
12. Scientific Computing
12.1. 12.1 Floating point arithmetic and error analysis
12.1.1. 12.1.1 Classical error analysis
12.1.2. 12.1.2 Forward and backward errors
12.1.3. 12.1.3 Rounding errors and floating point arithmetic
12.1.4. 12.1.4 The floating point arithmetic standard
12.2. 12.2 Linear systems of equations
12.2.1. 12.2.1 Direct methods for solving linear systems
12.2.2. 12.2.2 Iterative methods for linear systems
12.2.3. 12.2.3 Error analysis of linear algebraic systems
12.3. 12.3 Eigenvalue problems
12.3.1. 12.3.1 Iterative solutions of the eigenvalue problem
12.4. 12.4 Numerical program libraries and software tools
12.4.1. 12.4.1 Standard linear algebra subroutines
12.4.2. 12.4.2 Mathematical software