Numerical Algorithms - MU4IN910 (2022-2023)

News

First lecture on January 25th, 2023

Description of the course

This course is the natural continuation of the numerical part of MODEL course. It is a question of supplementing the knowledge in mathematical tools and algorithms in order to be able to solve concrete problems and of large sizes. We will study in particular algorithms and their implementation frequently used in the field of scientific computing and data science. The applications will be very diverse and may change each year: for example, we will see applications in finance (calculation of the price of options), in simulation of structures for 3D printing, in imaging (image compression), in deep learning (stochastic gradient algorithm), etc. We will endeavor for each algorithm to propose versions allowing an efficient implementation on parallel machines. The algorithms will be coded in MATLAB.

Tentative program per week

Floating-point arithmetic and rouding error analysis
Matrix computation
Introduction to continuous optimization
Nonlinear equations

Team of lecturers

Lectures: Stef Graillat
Tutorials/practicals: Stef Graillat

Schedule

Lectures: wednesday (8h30-10h30)
Tutorial: wednesday (10h45-12h45)
Practical: personal work
For rooms and planning, see planning of the master and full planning

Assigments, exams and grading

Grades will be computed as follows: exam (50%), praticals (50%)

Exam: ??
Re-take exam: ??

Documents

Moodle webpage for this course

Week 1:
- Lecture 1: Introduction to MATLAB
- Practical 1
Week 2:
- Lecture 2: Matrix computation
- Tutorial 2
Week 3:
- Lecture 3: Introduction to continuous optimization (1/2)
- Tutorial 3
Week 4:
- Lecture 4:Introduction to continuous optimization (2/2)
- Tutorial 4
Week 5:
- Lecture 5: Nonlinear equations
- Tutorial 5
Week 6:
- Tutorial 6: revision exercises - solutions

Software

Past exams

Exam and solutions

Bibliography

A First Course in Numerical Methods, Uri M. Ascher, Chen Greif, SIAM, 2011
Scientific Computing, An Introductory Survey, Michael T. Heath, Revised Second Edition, SIAM, 2018
Introduction to Scientific Computing and Data Analysis, Mark H. Holmes, Springer, 2016
Scientific Computing with Case Studies, Dianne P. O'Leary, SIAM, 2009
Linear Algebra and Learning from Data, Gilbert Strang, Wellesley-Cambridge Press, 2019
A Primer on Mathematical Modelling, Alfio Quarteroni, Paola Gervasio, Springer, 2020
Numerical Computing with MATLAB, Cleve Moler, SIAM, 2004
MATLAB Guide, Desmond J. Higham, Nicholas J. Higham, 3e édition, SIAM, 2017
Scientific Computing, An Introduction using Maple and MATLAB, Walter Gander, Martin Gander, Felix Kwok, Springer, 2014
Solving Problems in Scientific Computing Using Maple and MATLAB, Walter Gander, Jiri Hrebicek, 4e édition, Springer, 2004
Numerical Recipes. The Art of Scientific Computing, William Press, Saul Teukolsky, William Vetterling et Brian Flannery, 3rd Edition, Cambridge University Press, 2007
A Matrix Algebra Approach to Artificial Intelligence, Xian-Da Zhang, Springer, 2020
Linear Algebra and Optimization for Machine Learning, Charu C. Aggarwal, Springer, 2020
Introduction to the Tools of Scientific Computing, Einar Smith, Springer, 2021

Stef Graillat
(Last modification : January 19th, 2023)