Emphasis on large, sparse ill-conditioned linear and nonlinear problems. Description
of the most common techniques and computer laboratory experiments with some real
world data from applications in tomography, meteorology, and engineering. Background
in Linear Algebra and Numerical Analysis, and computing skills are assumed.
- Review of basic mathematical aspects and numerical algorithms for least
squares:
Singular Value Decomposition, perturbation analysis, QR and Lanczos
methods
- Rank-deficient and ill-conditioned problems
Direct and iterative methods
Regularization
- Nonlinear least squares problems
Gauss-Newton and Marquardt type methods. Separable problems
Bibliography to be used:
[1] Björck, Å.; "Numerical Methods for Least Squares Problems";
SIAM, 1996.
[2] Golub, G. and C.Van Loan; "Matrix Computations"; 3d ed., John
Hopkins, 1996.
[3] Hansen, P.H.;"Rank-deficient and Discrete Ill-posed Problems";
SIAM;1998.