Theoretical Numerical Analysis A Functional Analysis Framework /
Overall, the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references. - R. Glowinski, SIAM Re...
| Κύριοι συγγραφείς: | , |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
New York, NY :
Springer New York,
2001.
|
| Σειρά: | Texts in Applied Mathematics,
39 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 1 Linear Spaces
- 1.1 Linear spaces
- 1.2 Normed spaces
- 1.3 Inner product spaces
- 1.4 Spaces of continuously differentiable functions
- 1.5 Lp spaces
- 1.6 Compact sets
- 2 Linear Operators on Normed Spaces
- 2.1 Operators
- 2.2 Continuous linear operators
- 2.3 The geometric series theorem and its variants
- 2.4 Some more results on linear operators
- 2.5 Linear functional
- 2.6 Adjoint operators
- 2.7 Types of convergence
- 2.8 Compact linear operators
- 2.9 The resolvent operator
- 3 Approximation Theory
- 3.1 Interpolation theory
- 3.2 Best approximation
- 3.3 Best approximations in inner product spaces
- 3.4 Orthogonal polynomials
- 3.5 Projection operators
- 3.6 Uniform error bounds
- 4 Nonlinear Equations and Their Solution by Iteration
- 4.1 The Banach fixed-point theorem
- 4.2 Applications to iterative methods
- 4.3 Differential calculus for nonlinear operators
- 4.4 Newton’s method
- 4.5 Completely continuous vector fields
- 4.6 Conjugate gradient iteration
- 5 Finite Difference Method
- 5.1 Finite difference approximations
- 5.2 Lax equivalence theorem
- 5.3 More on convergence
- 6 Sobolev Spaces
- 6.1 Weak derivatives
- 6.2 Sobolev spaces
- 6.3 Properties
- 6.4 Characterization of Sobolev spaces via the Fourier transform
- 6.5 Periodic Sobolev spaces
- 6.6 Integration by parts formulas
- 7 Variational Formulations of Elliptic Boundary Value Problems
- 7.1 A model boundary value problem
- 7.2 Some general results on existence and uniqueness
- 7.3 The Lax-Milgram lemma
- 7.4 Weak formulations of linear elliptic boundary value problems
- 7.5 A boundary value problem of linearized elasticity
- 7.6 Mixed and dual formulations
- 7.7 Generalized Lax-Milgram lemma
- 7.8 A nonlinear problem
- 8 The Galerkin Method and Its Variants
- 8.1 The Galerkin method
- 8.2 The Petrov-Galerkin method
- 8.3 Generalized Galerkin method
- 9 Finite Element Analysis
- 9.1 One-dimensional examples
- 9.2 Basics of the finite element method
- 9.3 Error estimates of finite element interpolations
- 9.4 Convergence and error estimates
- 10 Elliptic Variational Inequalities and Their Numerical Approximations
- 10.1 Introductory examples
- 10.2 Elliptic variational inequalities of the first kind
- 10.3 Approximation of EVIs of the first kind
- 10.4 Elliptic variational inequalities of the second kind
- 10.5 Approximation of EVIs of the second kind
- 11 Numerical Solution of Fredholm Integral Equations of the Second Kind
- 11.1 Projection methods: General theory
- 11.2 Examples
- 11.3 Iterated projection methods
- 11.4 The Nyström method
- 11.5 Product integration
- 11.6 Projection methods for nonlinear equations
- 12 Boundary Integral Equations
- 12.1 Boundary integral equations
- 12.2 Boundary integral equations of the second kind
- 12.3 A boundary integral equation of the first kind
- References.
