Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.

Introduction to iterative methods
Model problems and Sobolev spaces
Abstract multilevel algorithms
Multigrid algorithms with nonnested spaces and varying forms
Construction of classes of smoothers
Application to second order elliptic problems
Perturbation of forms
Pseudodifferential operators of order minus one
Application to fourth order problems
Implementation, work estimates, and full multigrid
Appendices

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