37261 - Numerical Analysis

Learning outcomes

This course is meant to be an introduction to studying and numerically solving fundamental problems of scientific calculus. At the end of the course, the student is aware of techniques for the solution of computational problems, involving basic numerical calculus, data fitting and numerical linear algebra

Course contents

Finite numbers and floating point arithmetic; error analysis.

Brief introduction to data and functions approximation via polynomial interpolation or least squares approach. Some results on numerical integration.

Numerical linear algebra: LU and QR matrix factorizations. Singular Value Decomposition. Brief introduction to iterative methods for linear and non linear equations.

Readings/Bibliography

Any of the following books available at the Bologna University Libraries:

N. Higham, Accuracy and Stability of Numerical Algorithms, SIAM 2002.

D. Kincaid, E. W. Cheney, Numerical analysis: mathematics of scientific computing, 2nd ed. Brooks/Cole, 1996.

D. Bau, N. Trefethen, Numerical linear algebra, SIAM 1998.

G. W. Stewart, Afternotes on Numerical Analysis, SIAM 1996.

R. Bevilacqua, D.Bini, M. Capovani, O. Menchi, Introduzione alla matematica computazionale, Zanichelli, Bologna, 1987.

Course notes (in italian) published by Pitagora, Bologna.

Further Reading:

M. Overton, Numerical Computing with IEEE Floating Point Arithmetic, SIAM 2001.

Teaching methods

1. Class lectures
2. Exercises and tests
3. Seminars
4. Description of software environments for scientific computing

Assessment methods

Written test on the course contents, aimed at verifying the achievement of the learning outcomes, above described. The test questions concern all the course topics: questions may be purely conceptual and theoretical, or they may imply a reasoning connected to the rapid performing of short exercises.
The grade obtained in the Numerical Analysis module exam contributes to forming the arithmetic mean with the grade obtained in the Computational Statistics module exam: such a mean represents the overall grade of the Numerical Analysis integrated course.

Teaching tools

Text books available at the departmental libraries, course notes and material available at AMScampus

Links to further information

https://www.unibo.it/sitoweb/giulia.spaletta/news

Office hours

See the website of Giulia Spaletta