Optimization in solving elliptic problems

Content: Cover
 Half Title
 Title Page
 Copyright Page
 Preface
 Editor's Preface
 The Author
 The Editor
 Basic Notation
 Table of Contents
 Introduction
 1. Modern formulations of elliptic boundary value problems
 1.1. Variational principles of mathematical physics
 1.2. Variational problems in a Hilbert space
 1.3. Completion of a preHilbert space and basic properties of Sobolev spaces
 1.4. Generalized solutions of elliptic boundary value problems
 2. Projective-grid methods (finite element methods)
 2.1. Rayleigh-Ritz method
 2.2. Bubnov-Galerkin method and projective methods 2.3. Projective-grid methods (finite element methods)2.4. The simplest projective-grid operators
 2.5. Composite grids and triangulations
 local grid refinement
 3. Methods of solution of discretized problems
 asymptotically optimal and nearly optimal preconditioners
 3.1. Specificity of grid systems
 direct methods
 3.2. Classical iterative methods
 3.3. Iterative methods with spectrally equivalent operators
 optimal preconditioning
 3.4. Symmetrizations of systems
 3.5. Coarse grid continuation (multigrid acceleration of the basic iterative algorithm) 3.6. Some nonelliptic applications 4. Invariance of operator inequalities under projective approximations
 4.1. Rayleigh-Ritz method and Gram matrices
 4.2. Projective approximations of operators
 4.3. Spectral equivalence of grid operators defined on topologically equivalent triangulations
 4.4. Spectral equivalence of grid operators defined on composite triangulations with local refinements
 5. N-widths of compact sets and optimal numerical methods for classes of problems
 5.1. Approximations of compact sets and criteria for optimality of computational algorithms 3. Iterative methods with model symmetric operators3.1. Estimates of rates of convergence in the Euclidean space H(B) of the modified method of the simple iteration
 3.2. Estimates of the rate of convergence in the Euclidean space H(B2)
 3.3. Condition numbers of symmetrized linear systems
 generalizations for nonlinear problems
 3.4. A posteriori estimates
 3.5. Modifications of Richardson's iteration
 3.6. Use of orthogonalization
 3.7. Adaptation of iterative parameters
 3.8. Modified gradient methods
 3.9. Nonsymmetric model operators