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Third-Cycle Courses

Faculty of Engineering | Lund University

Details for the Course Syllabus for Course FMNN01F valid from Spring 2023

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General
Aim
  • The aim of the course is to make the postgraduate student familiar with concepts and methods from numerical linear algebra. In general there are ready-made program libraries available but it is important to be able to recognize types of input which may cause problems for the most common methods.
Contents
  • Norms.
    Singular value decomposition and numerical rank.
    QR factorization, the Gram-Schmidt process and Householder matrices.
    Least squares problems and pseudoinverses.
    Linear systems of equations and condition numbers.
    Positive definite matrices and Cholesky factorization.
    Numeric determination of eigenvalues.
Knowledge and Understanding
  • For a passing grade the doctoral student must
  • have demonstrated substantially better and more useful knowledge of numerical linear algebra than students who only have completed a regular basic course in scientific computing or linear algebra.
Competences and Skills
  • For a passing grade the doctoral student must
  • be able to implement algorithms for numerical linear algebra algorithms as computer code and to use them to solve applied problems.
Judgement and Approach
  • For a passing grade the doctoral student must
  • write logically well-structured reports, in adequate terminology, on weekly homework dealing with the construction and application of advanced algorithms in linear algebra.
Types of Instruction
  • Lectures
  • Voluntary assignments are given during the course. Feedback is given to those who hand in solutions.
Examination Formats
  • Oral exam
  • Failed, pass
Admission Requirements
Assumed Prior Knowledge
  • Calculus in several variables. Linear algebra including eigenvalues/vectors. Programming in Matlab or Python.
Selection Criteria
Literature
  • Trefethen, Lloyd N. & David Bau, I.: Numerical Linear Algebra. SIAM, 1997. ISBN 9780898713619.
Further Information
Course code
  • FMNN01F
Administrative Information
  • 2023-10-26
  • Maria Sandsten

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