NUMERICAL ANALYSIS II
cod. 14837

Academic year 2007/08
3° year of course - First semester
Professor
Academic discipline
Analisi numerica (MAT/08)
Field
Formazione modellistico-applicativa
Type of training activity
Characterising
48 hours
of face-to-face activities
6 credits
hub:
course unit
in - - -

Learning objectives

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A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern.

Prerequisites

<br /> <br />Numerical Analisys 1, Numerical Laboratory.

Course unit content

<br /> <br />Approximation of Functions and Modelling of Data: Interpolation by linear and cubic splines. Trigonometric polynomials. Orthogonal polynomials and least-squares approximations. Least-squares fits.<br />Numerical Integration: Gaussian quadrature. Adaptive quadrature. Multiple integrals.<br />Solution of Linear Systems of Equations:QR-decomposition. Least-squares solution of overdetermined linear systems. Basic iterative methods. Jacobi method and Gauss-Seidel method. Implementation of iterative methods. Conjugate gradient Algorithm<br />Eigenvalue problem. Localization of eigenvalues. The power method. The inverse power method. Eigenvalues and eigenvectors of a Tridiagonal matrix. Reduction of a general matrix to Hessemberg form. Householder transformations. The QR Algorithm for real Hessemberg matrices.<br />Solution of Nonlinear Equations: Secant method, False Position method. Newton’s method in two variables. Zeros of polynomials. Fixed-point methods. Rate of convergence.<br />Numerical Solution of Ordinary Differential Equations: Linear multistep methods. Adams methods. Predictor-corrector methods. Order and convergence for multistep methods. Finite-difference methods. Collocation methods.<br /> 

Full programme

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Bibliography

<br /> <br />A. Quarteroni, R. Sacco, F. Saleri, Matematica Numerica, (1998), SPRINGER;<br />G. Naldi, L. Pareschi, G. Russo, Introduzione al Calcolo Scientifico (metodi e applicazioni con Matlab), (2001) McGraw-Hill<br />G.Monegato, Fondamenti di Calcolo Numerico, CLUT, Torino.

Teaching methods

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Assessment methods and criteria

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Other information

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