04524 - Numerical Analysis

Learning outcomes

At the end of the course, the student has a deep knowledge of the numerical aspects of the mathematics in the applications.

Course contents

Principles of finite precision computation;

Review of the univariate and bivariate polynomial approximation theory; Bernstein basis functions;

Spline spaces and B-spline basis functions; convergence properties of the spline approximation; 

Knot-insertion / h-refinement, degree-elevation / p-refinement and k-refinement;

Interpolation and least squares approximation methods with spline functions (monovariate and bivariate case);

NURBS (Non Uniform Rational B-splines) spaces and RB-spline basis functions; 

Applications in CAD (Computer-Aided Design), CAM (Computer-Aided Manufacturing)and FEA (Finite Element Analysis) systems;

Outline of applications in 2D vector design, 3D graphics, and SCIVIS (SCIentific VISualization);

Exercises in Matlab/Octave environment on the previous topics.

Readings/Bibliography

1.N.J.Higham, Accuracy and Stability of Numerical Algorithms, second edition, SIAM, 2002.

2.M.J.D.Powell, Approximation theory and methods, Cambridge University Press, 1981.

3.C.de Boor, A practical guide to splines, Springer Verlag, 1978.

4.L.Piegl, W.Tiller, The NURBS book, 2nd Edition, Springer, 1997.

Teaching methods

Lectures and exercises in the computer laboratory. The exercises consist in the analysis / development and use of Matlab scripts, concerning the numerical methods proposed in class. The exercises will be guided by the teacher and aimed at a better understanding of the theory as well as increasing the student's computational skills.

Assessment methods

The exam consists in an oral discussion on the topics dealed with during the lessons and on the exercises carried out by the student during the course.

Teaching tools

Teacher's pantries on some topics, slides and Matlab code

Links to further information

http://www.dm.unibo.it/~casciola/html/anmat2021.html

Office hours

See the website of Giulio Casciola