Introduction
EXAMPLE: A TWO-POINT BOUNDARY VALUE PROBLEM: Introduction
Error, cost, and complexity
A minimal error algorithm
Complexity bounds
Comparison with the finite element method
Standard information
Final remarks
GENERAL FORMULATION: Introduction
Problem formulation
Information
Model of computation
Algorithms, their errors, and their costs
Complexity
Randomized setting
Asymptotic setting
THE WORST CASE SETTING: GENERAL RESULTS: Introduction
Radius and diameter
Complexity
Linear problems
The residual error criterion
ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS IN THE WORST CASE SETTING
Introduction
Variational elliptic boundary value problems
Problem formulation
The normed case with arbitrary linear information
The normed case with standard information
The seminormed case
Can adaption ever help?
OTHER PROBLEMS IN THE WORST CASE SETTING: Introduction
Linear elliptic systems
Fredholm problems of the second kind
Ill-posed problems
Ordinary differential equations
THE AVERAGE CASE SETTING: Introduction
Some basic measure theory
General results for the average case setting
Complexity of shift-invariant problems
Ill-posed problems
The probabilistic setting
COMPLEXITY IN THE ASYMPTOTIC AND RANDOMIZED SETTINGS: Introduction
Asymptotic setting
Randomized setting
Appendices
Bibliography.
