Numerical Linear Algebra

A.Y. 2016/2017
6
Max ECTS
60
Overall hours
SSD
MAT/08
Language
Italian
Learning objectives
This course focuses on the construction and analysis of numerical algorithms for solving the main linear algebra problems, such as the singular value decomposition, QR factorization, least square problems, linear systems, eigenproblems. These algorithms are the foundations of contemporary scientific computing and have applications in several fields of applied sciences and engineering.
Expected learning outcomes
Ability to construct and analyze the main algorithms of Numerical Linear Algebra. Development of implementation skills using Matlab and numerical verification of the theoretical results.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Course syllabus
1) Introduction. Vector, matrices, norms. Matlab. Singular Value Decomposition.
2) QR factorization. Gram-Schmidt orthogonalization. Least square methods.
3) Conditioning. Floating point arithmetic. Stability. Conditioning and stability of Least square methods.
4) Linear systems. Gaussian elimination, pivoting, stability. Cholesky.
5) Eigenvalues. Triangular and Hessenberg reduction. Rayleigh quotient, inverse iteration. QR algorithm.
6) Iterative methods. Arnoldi iteration. GMRES. Lanczos iteration. Conjugate gradient method. Preconditioning.
MAT/08 - NUMERICAL ANALYSIS - University credits: 6
Laboratories: 24 hours
Lessons: 36 hours
Professor: Lovadina Carlo
Professor(s)