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; numerical error; problem conditioning; method stability.

Polynomials and their representation in the language of vectors and matrices; their use in the approximation of data and functions, via interpolation or least squares fitting, and in numerical quadrature.

Numerical Linear Algebra: LU matrix factorization. Mention to QR matrix factorization. Some results on 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 UniBO Virtuale platform; lectures are not recorded. 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, Philadelphia, Pennsylvania, USA, 2002.

D. Kincaid, E. W. Cheney, Numerical analysis: mathematics of scientific computing, 3rd ed., American Mathematical Society, Providence, Rhode Island, USA, 2009.

D. Bau, N. Trefethen, Numerical linear algebra, SIAM, Philadelphia, Pennsylvania, USA, 1997.

G. W. Stewart, Afternotes on Numerical Analysis, SIAM, Philadelphia, Pennsylvania, USA, 1996.

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

Course notes (in italian) published by Pitagora: G.Spaletta, Analisi Numerica, Pitagora, Bologna, 2004.

Further Readings:

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

Teaching methods

1. Class lectures (obviously, complying with COVID-19 indications and the like)
2. Exercises in class and home assignments
3. Seminars
4. Description of a software environment 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. Students with specific learning disorders, special educational needs or disabilities can make use of all their compensatory and dispensatory aiding tools. 

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.

In the event of COVID-19 indications and the like, the assessment method may have to vary: in this case, students will be notified in advance and, in any case, during the lectures; in this case, moreover, the assessment procedures will be published in the teacher's NEWS and in the note contained in each exam enrolling list in Almaesami.

Teaching tools

Course notes and material to study and exercise available at the Virtuale platform (https://virtuale.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