Join Us On Monday, June 12, 2023!

Seminar by Dr. Hussam Al Daas, Senior Computational Mathematician, STFC-Rutherford Appleton Laboratory, will be held on June 12, 2023 in Rm 229, Manchester Hall at 2pm. The topic is “A Sparse Symmetric Factorization of a Sparse SPD Matrix”. Below please find the abstract:

Given a sparse SPD matrix A, we are interested in finding a decomposition A = L T L, where L is sparse rectangular (tall and skinny) and has O(nnz(A)) nonzeros where nnz(A) is the number of nonzeros in A. The matrix L may not be unique but this is not important as we need only one solution.
Given a sparsity pattern of a solution L, finding the values is a simple quadratic optimization problem. The tricky question is to find a sparsity structure of a solution. Finding sparsity patterns of potential solutions can be cast as a clique-finding problem in a graph. The origin of my interest in this problem goes back to building efficient preconditioners for sparse systems of equations. I will describe the connection with preconditioning and my failed attempts to solve the problem!