Title | Frontiers in Numerical Analysis [electronic resource] : Durham 2002 / edited by James F. Blowey, Alan W. Craig, Tony Shardlow |
---|---|
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003 |
Connect to | http://dx.doi.org/10.1007/978-3-642-55692-0 |
Descript | XIV, 354 p. 32 illus., 1 illus. in color. online resource |
Subgrid Phenomena and Numerical Schemes -- 1 Introduction -- 2 The Continuous Problem -- 3 From the Discrete Problem to the Augmented Problem -- 4 An Example of Error Estimates -- 5 Computational Aspects -- 6 Conclusions -- References -- Stability of Saddle-Points in Finite Dimensions -- 1 Introduction -- 2 Notation, and Basic Results in Linear Algebra -- 3 Existence and Uniqueness of Solutions: the Solvability Problem -- 4 The Case of Big Matrices. The Inf-Sup Condition -- 5 The Case of Big Matrices. The Problem of Stability -- 6 Additional Considerations -- References -- Mean Curvature Flow -- 1 Introduction -- 2 Some Geometric Analysis -- 3 Parametric Mean Curvature Flow -- 4 Mean Curvature Flow of Level Sets I -- 5 Mean Curvature Flow of Graphs -- 6 Anisotropic Curvature Flow of Graphs -- 7 Mean Curvature Flow of Level Sets II -- 7.2 Anisotropic Mean Curvature Flow of Level Sets -- References -- An Introduction to Algorithms for Nonlinear Optimization -- 1 Optimality Conditions and Why They Are Important -- 2 Linesearch Methods for Unconstrained Optimization -- 3 Trust-Region Methods for Unconstrained Optimization -- 4 Interior-Point Methods for Inequality Constrained Optimization -- 5 SQP Methods for Equality Constrained Optimization -- 6 Conclusion -- GniCodes - Matlab Programs for Geometric Numerical Integration -- 1 Problems to be Solved -- 2 Symplectic and Symmetric Integrators -- 3 Theoretical Foundation of Geometric Integrators -- 4 Matlab Programs of โGniCodesโ -- 5 Some Typical Applications -- References -- Numerical Approximations to Multiscale Solutions in PDEs -- 1 Introduction -- 2 Review of Homogenization Theory -- 3 Numerical Homogenization Based on Sampling Techniques -- 4 Numerical Homogenization Based on Multiscale FEMs -- 5 Wavelet-Based Homogenization (WBH) -- 6 Variational Multiscale Method -- References -- Numerical Methods for Eigenvalue and Control Problems -- 1 Introduction -- 2 Classical Techniques for Eigenvalue Problems -- 3 Basics of Linear Control Theory -- 4 Hamiltonian Matrices and Riccati Equations -- 5 Numerical Solution of Hamiltonian Eigenvalue Problems -- 6 Large Scale Problems -- 7 Conclusion -- References