NUMERICAL METHODS AND APPLICATIONS B
Numerical Analysis
Oral exam and an optional project implemented in Matlab.
Definition and numerical solution of inverse problems
Discrete least-square problems: minimum norm solution, singular value decomposition (SVD), truncated SVD (TSVD), pseudo-inverse, Golub-Kahan algorithm to compute the SVD, Landweber iteration.
Ill-posed problems and regularization: filtering by TSVD, Tikhonov method and SVD filtering. Strategies for estimating the regularization parameter: discrete Picard condition, discrepancy principle, L-curve and GCV. Regularization iterative methods (e.g. Landweber and conjugate grandients for normal equations).
Convolution and discrete Fourier transform by fast Fourier transform. Compression and deconvolution of signals and images.
The numerical methods and some applications will be implemented and tested using MatLab.
G. H. Golub,C. F. Van Loan, “Matrix Computation”, Johns Hopkins.
Per Christian Hansen, “Rank-Deficient and Discrete Ill-Posed Problems”, SIAM.
P. C. Hansen, J. G. Nagy, and D. P. O'Leary, “Deblurring Images: Matrices, Spectra, and Filtering”, SIAM.
Front lectures.
Borrowed from
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