Elements of numerical analysis - (5 cfu)

Prof. Alessandra Aimi Tel. 0521 906944 - Fax. 0521 906950
  E-mail. alessandra.aimi@unipr.it
 


Finalità

OBJECTIVES: introduction to the basic methods and algorithms of Numerical Analysis

Programma

Error analysis
Conditioning of a problem and stability of an algorithm. Errors in computations. Rounding errors and floating-point arithmetic.

Polynomial interpolation
Lagrange form of the interpolating polynomial. Divided differences and the Newton form of the interpolating polynomial. Interpolation Polynomials and Raimender Terms for Equidistant Nodes. Stability of the interpolating polynomial. Divergence of sequences of interpolation polynomials. Hermite interpolation. Linear spline interpolation. Convergence.

Numerical integration
Interpolatory numerical integration. Newton-Cotes formulas. Errors of quadrature formulas. Automatic integration.

Numerical linear algebra
Condition number. Triangular system solution. Gaussian elimination. Pivoting and scaling. Direct factorization methods. LU-decomposition. Determinant and invers of a square matrix. Tridiagonal matrices.

Numerical solution of nonlinear equations
Conditioning of a nonlinear equation. Bisection method. Newton’s method. Convergence of Newton’s method. Rate of convergence. Stop tests. Roots of algebraic polynomials. Newton-Horner method.

Introduction to MATLAB
Matlab as computational environment. Array and matrices. Files, functions and data structures. Matlab as programming language. Diagrams. Graphics. Matlab functions for the solution of some Numerical Analysis problems. Matlab as a tool to implement and analyse numerical algorithms.

Modalità d'esame

Written exam

Testi consigliati

G. Naldi, L. Pareschi, G. Russo, Introduzione al Calcolo Scientifico. Metodi e applicazioni con Matlab, Mc Graw-Hill, 2001
V. Comincioli, Analisi Numerica, Mc Graw-Hill, 1995
A. Quarteroni, R. Sacco, F. Saleri, Matematica Numerica, Springer
J. Stoer, Introduzione all’analisi numerica, Vol. I, Zanichelli, 1974
W. J. Palm, MATLAB 6 per l’ingegneria e le scienze. McGraw-Hill, 2001


Ultimo aggiornamento: 24-07-2006


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