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02023 - Numerical Computing

Academic Year 2021/2022

                
                        Docente:
                        Valeria Simoncini
                    
                        Credits:
                        10
                    
                        SSD:
                        MAT/08
                    
                        Language:
                        Italian
                    
                        Teaching Mode:
                        Traditional lectures
                        
                            Campus:
                            Bologna
                        
                            Corso:
                            First cycle degree programme (L) in
                            Mathematics (cod. 8010)

                            Teaching resources on Virtuale

Learning outcomes

At the end of the course, the student will be confident with the basic foundations of Scientific Computing. She/he knows and can use the principal algorithmic methods for numerically solving problems on the computer. She/he is able to autonomously implement algorithms and use principal data stractures.

Course contents

Floating point arithmetic.

Numerical methods for the solution of a nonlinear equation.

Numerical linear algebra: direct methods for the solution of a linear system; iterative methods for the solution of a linear system; Householder reflections and Givens rotations; orthogonal factorizations: QR and linear least squares solution. Numerical methods for eigenvalues and eigenvectors computation.

Data approximation: polinomial and piecewise polinomial functions; interpolation and least squares approximation.

Numerical integration: quadrature formulas of Newton-Cotes types and their composite variants.

Nonlinear equations: bisection, newton, fixed point methods. Implementation and convergence analysis.

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.

additional texts
- "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.
and others

Lecture notes

Teaching methods

Use of blackboard in class, computer tablet writing and other computer software.
Extra material provided in the course website.

Notes on Virtuale.

Assessment methods

Lab Test, one for each course period.

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.

Teaching tools

ex cathedra teaching plus computer lab sessions.

Links to further information

http://www.dm.unibo.it/~simoncin/Calcolo_Numerico1516.html

Office hours

See the website of Valeria Simoncini