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; problem conditioning; method stability.

Introduction to data and functions approximation via polynomial interpolation or least squares fitting. Some results on numerical integration.

Numerical linear algebra: LU matrix factorization. Brief introduction to QR matrix factorization. Brief introduction to Singular Value Factorization.

Mention to iterative methods for linear and non linear equations.

Readings/Bibliography

The material developed in class, useful for exam preparation, is made available to students enrolled in the course through the IOL platform.
Any other material/text on fundamentals of Numerical Calculus/Analysis is obviously also useful, both for the exam preparation and for an in-depth study: the following (not compulsory) books are recommended because (besides being excellent texts) they are available at the UniBo 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.

It is an open-book test; mobile phones and internet connection are prohibited.

The test total time, including, in particular, its illustration by the teacher, does not generally exceed 90 minutes (120 minutes maximum).

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

Course notes and material available at the IOL platform (https://iol.unibo.it) and text books available at the departmental libraries.

Links to further information

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

Office hours

See the website of Giulia Spaletta