2013 SIAM Gene Golub SIAM Summer School
10th Shanghai Summer School on Analysis and Numerics in Modern Sciences

Programming Assignment

Test Matrices

  1. A matrix pencil A-\lambda B arises from solving Korn-Sham equation for C6H6 by SCF. It is a reduced one (of 25x2500) for fast experimenting. The unreduced one is of 14895x14895. Courtesy of Prof. Yunkai Zhou (SMU).
  2. A matrix pencil A-\lambda B arises from solving the Laplacian eigenvalue problem in a barbell shaped domain. Courtesy of Prof. Qiang Ye (U. Kentucky) and Dr. Patrick Quillen (Mathworks).
  3. A linear response eigenvalue problem arises from the linear response analysis for Na2 using plane-waves as a basis set and pseudopotentials. It is generated by the Quantum ESPRESSO. While here both K and M are dense, they are never meant to be formed explicitly, but exist implicitly through matrix-vector product. Nonetheless, they are formed for easy experimenting in MATLAB. Courtesy of Prof. D. Rocca (Universite de Lorraine - CNRS)

MATLAB functions

  1. Steepest Descent Methods (a sample driver):

  2. Conjugate Gradient Methods (a sample driver):

  3. Steepest Descent Methods for the linear response eigenvalue problem: a sample driver and the function.

  4. Conjugate Gradient Methods for the linear response eigenvalue problem: a sample driver and the function. Also needed is KM.m.

  5. Conjugate Gradient Methods for the hyperbolic quadratic eigenvalue problem: a sample driver and the function. Also needed is HQEP.m.

  6. Auxiliary MATLAB functions:

Assignment:

Program various extended methods (i.e., enlarge search subspaces to a higher order Krylov subspaces) by modifying the relevant MATLAB functions above.

Written Assignments