Numerical Linear Algebra

Numerical Linear Algebra


Academic year 2011/2012
PhD program in Mathematics UC-UP
Department of Mathematics
Faculty of Science and Technology, University of Coimbra
Teacher: Adérito Araújo

Schedule and attendance of students

Class
Monday
Tuesday
Wednesday
Thursday
Friday




9:00-13:00
Room:
Attendance
Monday
Tuesday
Wednesday
Thursday
Friday





14:00-15:00
Office:


Syllabus

    1. Introduction

    2. Basic operations and norms

    3. Orthogonality and the SVD

    4. Introduction to error analysis

    5. Linear systems

    6. Linear Least Squares

    7. Eigenvalue problems

    8. Iterative methods

    9. Sparse matrices

    10. Introduction to High-Performance Computing

    11. Projects and applications


Bibliography
Text
  • L. N. Trefethen, D. Bau. Numerical Linear Algebra. SIAM 1997.<\li>
Recommended Texts
  • J. W. Demmel. Applied Numerical Linear Algebra. SIAM 1997.
    Also aimed at a first year graduate audience, but has a more practical flavor than the main text.
  • G. H. Golub, C. F. Van Loan. Matrix Computations. John Hopkins University Press 1996.
    Very complete, if not encyclopedic, book on matrix computations.
  • Yousef Saad. Iterative Methods for Sparse Linear Systems. PWS Publishing, 1996. Comprehensive work on methods for iterative methods.
Templates Other Reading
  • A. Bjorck. Numerical Methods for Least Squares Problems. SIAM 1996.
    Comprehensive work on methods for linear least squares problems.
  • W. Briggs. A Multigrid Tutorial, SIAM, 1987.
    A good introduction to multigrid methods.
  • N. J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM 2002 (2nd edition).
    Comprehensive rounding error analysis for linear equations and least squares problems.


Assessment

The final exams are in the following dates.

    Hour
    Final exam
    Hour
    Final exam 2
    14:30
    June 2012
    14:30
    July 2012


Homeworks, projects and class support files


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