Matrix operations of almost linear complexity for computing eigenpairs of large dimensional problems
 
 
Description: 
We consider the numerical solution of a large eigenvalue problem resulting from a nite rank discretization of an integral operator. We are interested in computing a few eigenpairs, with an iterative method, so a matrix representation that allows for fast matrix-vector products is required. Hierarchical matrices are appropriate for this setting, and also provide cheap LU decompositions required in the spectral transformation technique. We illustrate the use of freely available software tools to address the problem, in particular SLEPc for the eigensolvers and HLib for the construction of H-matrices. We develop analytical expressions for the approximate degenerate kernels and deduce error upper bounds for these approximations. Numerical tests show the bene ts of the data-sparse representation compared to standard storage schemes, in terms of computational cost as well as memory requirements.
 
This work was done with the collaboration of A. L. Nunes, J. E. Roman and M. Ahues.
Date:  2012-10-24
Start Time:   11:30
Speaker:  Paulo Vasconcelos (CMUP)
Institution:  University of Porto
Place:  Room 5.5 (DMUC)
Research Groups: -Numerical Analysis and Optimization
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