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B006819 - NUMERICAL ANALYSIS
Main information
Teaching Language
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2014-15
Course year
Third year - Annualità singola
Belonging Department
Statistics, IT and its applications "G. Parenti" (DISIA)
Course Type
Single education field course
Scientific Area
MAT/08 - NUMERICAL ANALYSIS
Credits
9
Teaching Hours
84
Teaching Term
22/09/2014 ⇒ 12/06/2015
Attendance required
No
Type of Evaluation
Final Grade
Course program
show
Lectureship
Teaching Language
Italian
Suggested readings (Search our library's catalogue)
L.Brugnano, C.Magherini, A.Sestini. Calcolo numerico, seconda edizione. Master, Universita' e Professioni, Firenze, 2010.
Learning Objectives
Conoscenze:
il corso si propone l'obiettivo di fornire gli strumenti di base di più comune utilizzo nel calcolo scientifico, con particolare enfasi sugli aspetti legati alla loro efficiente implementazione su calcolatore.
Competenze acquisite:
conoscenza dei metodi di base del calcolo scientifico.
Capacità acquisite al termine del corso:
capacita' di risolvere problemi di caclolo scientifico di base su calcolatore.
il corso si propone l'obiettivo di fornire gli strumenti di base di più comune utilizzo nel calcolo scientifico, con particolare enfasi sugli aspetti legati alla loro efficiente implementazione su calcolatore.
Competenze acquisite:
conoscenza dei metodi di base del calcolo scientifico.
Capacità acquisite al termine del corso:
capacita' di risolvere problemi di caclolo scientifico di base su calcolatore.
Prerequisites
Courses required: Analysis I: Integral and Differential Calculus, Linear Algebra, Programming.
Recommended Courses: Analysis I: Integral and Differential Calculus, Linear Algebra, Programming.
Recommended Courses: Analysis I: Integral and Differential Calculus, Linear Algebra, Programming.
Teaching Methods
Credits: 9
Oral exam,
hours: 84
Oral exam,
hours: 84
Type of Assessment
Oral exam with report
intermediate for attending students
intermediate for attending students
Course program
And finite arithmetic errors: errors of discretization, convergence errors, round-off errors, conditioning of a problem. The language Matlab.Radici of an equation: the bisection method, stopping criteria and conditioning of the problem, order of convergence, Newton's method, local convergence, the case of multiple roots, quasi-Newton methods. Solution of linear systems: simple cases, the LU factorization of a matrix, computational cost, diagonally dominant matrix, symmetric matrices and positive definite, LDL ^ T factorization, pivoting, conditioning of the problem, QR factorization and overdetermined linear systems. Basic iterative methods for solving linear systems: motivation, the Jacobi method, the Gauss-Seidel, splitting regular matrices. Outline of the basic methods for solving systems of nonlinear equations. Approximation of functions: polynomial interpolation, Lagrange shape and form of Newton interpolation error, conditioning of the problem, the Chebyshev abscissas, spline interpolation, cubic spline, polynomial approximation to the minimum quadrati.Formule quadrature: Newton-Cotes formulas , error and composite formulas, formulas adattative.Metodi for research of the eigenvalues of a matrix: the power method, applied to the calculation of "Google pagerank".