NUMERICAL ANALYSIS

Degree course: 
Corso di Second cycle degree in Physics
Academic year when starting the degree: 
2014/2015
Year: 
1
Academic year in which the course will be held: 
2014/2015
Course type: 
Supplementary compulsory subjects
Credits: 
6
Period: 
Second semester
Standard lectures hours: 
60
Detail of lecture’s hours: 
Lesson (60 hours)
Requirements: 

Laboratory of computational mathematics.

Assessment: 
Voto Finale

Error analysis, estimates of eigenvalues and solving linear systems.

Analysis of error: representation of numbers on the computer and impersonation error; analytical error inherent algorithmic; use of graphs for the analysis of the error. Iterative method for zeros of functions in the case of real functions in one variable: bisection method; methods of functional iteration convergence theorem and the convergence order of a method; Newton's method with some convergence and results on the order of method; secant method and false position. Basic linear algebra: eigenvalues, eigenvectors and spectral radius; vector norms and their property; induced matrix norm and their relationships with the spectral radius; Hermitian and positive definite matrices. Iterative methods for linear systems: stationary iterative methods; convergence theorem; asymptotic rate of convergence; methods of Jacobi and Gauss-Seidel with convergence results for certain classes of matrices. Direct methods for linear systems: conditioning of a linear system; triangular systems; Gaussian elimination; Elementary matrices and matrix factorizations. LU factorization with partial pivoting, and total; Cholesky method; QR factorization and Houselder arrays.
Frontal lectures.

“Metodi numerici per l'algebra lineare” di D. Bini, M. Capovani and O. Menchi, casa ed. Zanichelli. “Metodi numerici” di R. Bevilacqua, D. Bini, M. Capovani and O. Menchi, casa ed. Zanichelli.
Written and oral examination.

Borrowed from

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Degree course in: MATHEMATICS