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NUMERICAL METHODS AND APPLICATIONS B

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2016/2017
Year: 
1
Academic year in which the course will be held: 
2016/2017
Course type: 
Supplementary compulsory subjects
Credits: 
8
Period: 
Second semester
Standard lectures hours: 
80
Detail of lecture’s hours: 
Lesson (80 hours)
Requirements: 

Numerical Analysis

Final Examination: 
Orale

Oral exam and an optional project implemented in Matlab.

Assessment: 
Voto Finale

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.

Professors

DONATELLI MARCO

Borrowers