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.