*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

### Schedule

### 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:**
**Week 2:**
**Week 3:**
**Week 4:**
**Week 5:**
**Week 6:**

### Software

### Past exams

### 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)