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Scientific computing - 4AMMA441

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  • Number of hours

    • Lectures : 18.0
    • Tutorials : -
    • Laboratory works : 9.0
    • Projects : -
    • Internship : -
    • Written tests : -
    ECTS : 2.5
  • Officials : Laurent LEFEVRE

Goals

This course is an introduction to scientific computing and the specificities related with floating point arithmetics and calculus on computers. It aims at providing the students a working knowledge in the analysis of:
*well-posedness or ill-conditioning
*numerical stability or unstability of numerical algorithms
*accuracy and complexity of numerical algorithms. Les étudiants sont amenés à évaluer

These concepts are then illustrated on the following problems:
*iterative methods for non linear algebraic equation
*Numerical integration of ordinary differential equations (initial value problems)

Content

*Computer arithmetics and round-off errors
**Floating point arithmetics
**Basic operations and round-off errors
**Error propagation, conditioning and numerical stability
*Iterative methods
**Fixed point theorems
**Order of convergence and convergence acceleration methods
**Application to non linear equations
*Numerical integration of ODEs
**Existence and conditioning results
**One-step methods
**Multi-steps methods
**Stiff problems

Prerequisites

Any undergraduate courses in calculus and linear algebra

Tests



Calendar

The course exists in the following branches:

  • Curriculum - EIS - Semester 7
see the course schedule for 2020-2021

Additional Information

Course ID : 4AMMA441
Course language(s): FR

The course is attached to the following structures:

  • Team

You can find this course among all other courses.

Bibliography

  • Accuracy and Stability of Numerical Algorithms, N.J. Higham, SIAM Publications, Philadelphia, 1995.
  • Analyse Numérique, Sous la direction de J. Baranger, Hermann 1991.
  • Introduction à l'analyse numérique, J. Rappaz et M. Picasso, Presses Polytechniques Romandes, 2004

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Date of update May 29, 2015

Université Grenoble Alpes