Project


The project is worth 100 points. The due date is Friday December 3, 2004. Do not wait until the last minute!
    A common feature of virtually all large linear problems is that they cannot be solved directly by existing computers. Many of these large linear problems require solutions that involve hundreds of thousands of unknowns. For such problems, approximation techniques are used to find solutions. This is commonly done by finding a problem of much smaller dimension which can be solved directly and whose solution can be used to generate an acceptable approximation of the original problem. Important collections of techniques of this kind are called Krylov subspace methods.

      Each paper/project should contain the following:
    • A brief description of Krylov subspaces and how they are used to solve large linear problems.
    • A more indepth description of a Krylov subspace method and how it is used to solve either an eigenvalue problem or a linear system. Some specific Krylov subspace methods: Arnoldi, Lanczos, GMRES, CG, MINRES.
    • An example written in MATLAB or Maple of a Krylov subspace method.
    • Description of a real world application.
    • List of references. You must use more than one source. I will not accept a website as a reference.

      Some articles and books to get you started:
    • J. Demmel, Applied Numerical Linear Algebra, SIAM Philadelphia PA, 1997.
    • G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. John Hopkins 1996.
    • I. C. F. Ipsen and C. D. Meyer, ``The idea behind krylov methods'', The American Mathematical Monthly, Vol. 105, No. 10 pp 889-899, December 1998.
    • Y. Saad, Iterative Methods for Sparse Linear Systems, PWS 1996.
    • Y. Saad, Numerical Methods for Large Eigenvalue Problems, Manchester Univ. Press 1992. A copy is avaiable on Saad's website .