NUMERICAL ANALYSIS I
cod. 1003814

Academic year 2007/08
2° year of course - Second semester
Professor
Academic discipline
Analisi numerica (MAT/08)
Field
Formazione modellistico-applicativa
Type of training activity
Characterising
60 hours
of face-to-face activities
6 credits
hub: -
course unit
in - - -

Learning objectives

  Numerical analysis, in essence, is a branch of mathematics which deals with the numerical and therefore constructive solution of problems, formulated and studied in other branches of mathematics. One of aims of this course is to present background material of several numerical methods in branches of mathematics with which numerical analysis has made its principal contacts.

Prerequisites

 First principles of Analysis and Geometry

Course unit content

 Stability and Conditioning. Roundoff Erroes and Floating-point Arithmetic. Interpolation and Approximation. Polynomial interpolation. Hermite interpolation. Runge phenomenon for standard polynomial interpolation. Splines. Least-square approximations. Trigonometric interpolation.Solution of linear system of equations. Gauss elimination. Operations counts. Pivoting and Scaling in Gauss elimination. LU decompositions. Cholesky decomposition. QR decomposition. Least-squares solution of over-determined linear systems. Numerical integration. Newton-Cotes Formulas. Composite formulas. Error estimate. Adaptive quadrature.Solution non-linear equations. Bisection. Newton method in one variable. Secant method. Construction. Practical considerations.

Full programme

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Bibliography

 A.Quarteroni, R.Sacco, F.Saleri, Matematica Numerica, Springer-Verlag. G.Naldi, L.Pareschi, G. Russo, Introduzione al Calcolo Scientifico (metodi e applicazioni con Matlab),  McGraw-Hill.G.Monegato, Fondamenti di Calcolo Numerico, CLUT, Torino.William J. Palm III, Introduction to MATLAB 7 for engineerings,  McGraw-Hill.

Teaching methods

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Assessment methods and criteria

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Other information

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