Numerical Analysis and Optimization: An Introduction to Mathematical Modelling and Numerical SimulationOUP Oxford, 24 mai 2007 - 455 pages This text, based on the author's teaching at École Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Covering the finite difference method; variational formulation of elliptic problems; Sobolev spaces; elliptical problems; the finite element method; Eigenvalue problems; evolution problems; optimality conditions and algorithms and methods of operational research, and including a several exercises throughout, this is an ideal text for advanced undergraduate students and graduates in applied mathematics, engineering, computer science, and the physical sciences. |
Table des matières
| 1 | |
| 31 | |
| 65 | |
| 79 | |
5 Mathematical study of elliptic problems | 109 |
6 Finite element method | 149 |
7 Eigenvalue problems | 205 |
8 Evolution problems | 231 |
9 Introduction to optimization | 277 |
10 Optimality conditions and algorithms | 297 |
11 Methods of operational research Written in collaboration with Stéphane Gaubert | 347 |
Review of hilbert spaces | 399 |
Matrix Numerical Analysis | 405 |
Index | 451 |
Index notations | 455 |
Autres éditions - Tout afficher
Numerical Analysis and Optimization: An Introduction to Mathematical ... Grégoire Allaire Affichage d'extraits - 2007 |
Numerical Analysis and Optimization: An Introduction to Mathematical ... Grégoire Allaire Aucun aperçu disponible - 2007 |
Expressions et termes fréquents
algorithm allows apply approximation associated assume basis belongs bilinear form boundary conditions bounded calculate called Chapter closed Consequently consider constant constraints continuous convergence convex cost deduce defined definition denote depends derivative difference differentiable dimension Dirichlet discrete easily effect eigenvalues energy equality equation equivalent example Exercise exists explicit fact Figure Finally finite element method flow function given gives gradient heat Hilbert space hypothesis idea implies inequality initial integration introduce iteration Laplacian lemma linear linear system mapping matrix mesh method minimization necessary norm numerical obtain open set operator optimal particular positive practice problem Proof proposition prove regular Remark respect result satisfies scheme sense sequence Show simple solution solve stability step symmetric term theorem unique solution variational formulation vector verify vertices wave weak zero