SSP Project Summary:

Investigation of the eigenvalue structure of matrices for modelling satellite magnetic data

Student

Supervisors

Kathy Whaler, Department of Geology and Geophysics, University of Edinburgh

CG does not converge particularly well for this problem. There are two approaches that could be investigated. The simpler one is to explore various methods of preconditioning the system, which has often been successful in improving convergence.

The more time-consuming part of the project involves an investigation of the matrix's eigenvalue structure close to zero which is related to the best choice of damping factor for the matrix. Similar problems often have a small eigenvalue 'tail', or it is found that the matrix's eigenvalues condense towards zero. Damping in this case involves adding a (positive) number to the diagonal elements of the matrix to be inverted, whose value is chosen to exceed, and therefore damp out the effects of, the small eigenvalues. For this the student would write, from scratch, a conjugate gradient method for finding the eigenvalues and again this should be parallelised using OPENMP.

If time is available at the end, the student could compare performance of the OpenMP version of the matrix multiply with the MPI version or investigate other methods (e.g. Accelerated CG,PARPACK) of finding the eigenvalue structure of the matrix close to zero.

Webpage maintained by mario@epcc.ed.ac.uk