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NUMERICAL METHODS AND APPLICATIONS B

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2022/2023
Year: 
1
Academic year in which the course will be held: 
2022/2023
Course type: 
Supplementary compulsory subjects
Credits: 
8
Period: 
First Semester
Standard lectures hours: 
64
Detail of lecture’s hours: 
Lesson (64 hours)
Requirements: 

Basic course in numerical analysis.

Final Examination: 
Orale

Oral examination and project implemented in Matlab.

Assessment: 
Voto Finale

Students will acquire the basic knowledge in order to model and to solve ill-posed problems.

Discrete least-square problems and SVD.

Ill-posed problems and regularization with application to imaging.

Introduction to machine learning.

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. (24 h)

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 (Landweber method and conjugate grandients for normal equations). Convolution and discrete Fourier transform by fast Fourier transform. Compression, segmentation and deconvolution of signals and images. (30 h)

Introduction to machine learning showing that the main idea of machine learning can be
traced back to the regularization of a ill-posed inverse problem
depending on the the choice of the data fidelity measure and the predicting
model. (10 h)

The numerical methods and some applications will be implemented and tested using MatLab.

Convenzionale

Front lectures with some computer lab supplementary lessons.

Meeting by appointment.

Professors

DONATELLI MARCO

Borrowers