Coursebooks 2017-2018

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Computational linear algebra

MATH-453

Lecturer(s) :

Massei Stefano

Language:

English

Summary

This course provides an overview of state-of-the-art techniques for solving large-scale linear algebra problems, as they typically arise in applications. A central goal of this course is to give the ability to choose a suitable solver for a given application.

Content

Introduction

Sources of large-scale linear algebra problems. Recap of required linear algebra concepts.

Eigenvalue problems

Krylov subspace methods. Singular value problems. Preconditioned iterative methods. 

Linear systems

Direct sparse factorizations. Krylov subspace methods and preconditioners.

Matrix functions

Theory and algorithms.

Keywords

linear systems, eigenvalue problems, matrix functions

Learning Prerequisites

Required courses

Linear Algebra, Numerical Analysis

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Ex cathedra lecture, exercises in the classroom and with computer

Expected student activities

Attendance of lectures.

Completing exercises.

Solving problems on the computer.

Assessment methods

Oral examination.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Resources

Bibliography

Lecture notes will be provided by the instructor. Complimentary reading:

H. Elman, D. J. Silvester, and A. J. Wathen. Finite elements and fast iterative solvers: with applications in incompressible fluid dynamics. Oxford University Press, 2005.

G. H. Golub and C. Van Loan. Matrix computations. Johns Hopkins University Press, 1996.

Y. Saad. Iterative methods for sparse linear systems. Second edition. SIAM, 2003.

 

Ressources en bibliothèque

In the programs

Reference week

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8-9     
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Under construction
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German