- Docente: Valeria Simoncini
- Credits: 9
- SSD: MAT/08
- Language: Italian
- Moduli: Valeria Simoncini (Modulo 1) Giulio Casciola (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: First cycle degree programme (L) in Mathematics (cod. 8010)
Course contents
Module I Floating point arithmetic. Numerical linear algebra:
direct methods for the solution of a linear system; iterative
methods for the solution of linear systems; Householder reflections
and Givens rotations; orthogonal factorizations: QR and Singular
Value Decomposition; linear least squares solution. Numerical
methods for eigenvalue and eigenvector computation. Simple examples
from physical, engineering and social science applications.
Module II: Data approximation: polynomial and piecewise polynomial
functions; interpolation and least squares approximation. Numerical
methods for the solution of a nonlinear equation.
Numerical integration: quadrature methods
Readings/Bibliography
- "Matematica Numerica", A. Quarteroni, R. Sacco, F. Saleri, III ed., Springer 2008 e succ. - "Analisi Numerica - metodi modelli applicazioni", V. Comincioli, McGraw-Hill 1995. - "Introduction to Numerical Analysis", J. Stoer, R. Bulirsch, II ed., Springer 1993 e succ. - "Applied Numerical Linear Algebra", J. W. Demmel, SIAM 1997. - "Metodi numerici per l'algebra lineare", D. Bini, M. Capovani, O. Menchi, Zanichelli 1988. - "Accuracy and Stability of Numerical Algorithms", N. J. Higham, SIAM 1996. - "Matrix computations", G. H. Golub e C. F. Van Loan, The Johns Hopkins University Press, 1996 e succ. "Numerical methods for unconstrained optimization and nonlinear equations", J.E. Dennis, R.B. Schnabel, Prentice Hall, Englewood Cliffs, NJ, 1983. "Metodi Numerici", Bevilacqua, Bini, Capovani, Menchi, ed Zanichelli, 1992.
Teaching methods
Use of blackboard in class and slides.
Extra material provided in the course website.
Assessment methods
Module I: Written test on the topics presented during the semester,
including the pseudo-code implementation of simple algorithms. The
written test is followed by an oral test, on the same topics.
Module II: Oral discussion of a computer lab project, and an
oral exam.
The final grade will be the average of the marks for the two
modules.
Teaching tools
ex cathedra teaching plus computer lab sessions.
Links to further information
http://www.dm.unibo.it/~simoncin/Calcolo_Numerico.html
Office hours
See the website of Valeria Simoncini
See the website of Giulio Casciola