Thursday, February 10 at 3 PM in the Atrim (Little 339), Sukanya Krishnaswamy
will give the following talk:

Abstract:
The problem of solving linear systems of equations Ax = b, where the
coefficient matrix A is sparse and symmetric, is at the core of several
engineering, scientific and financial applications. In this paper
we implement and test a non-adjacent row and column exchange scheme
to reduce the profile of a sparse, symmetric matrix. The profile of a
matrix is the number of elements lying between the first nonzero
in each row and the diagonal, plus the diagonal
elements. Profile storage is useful when the matrix is either
moderately sparse or has nonzero entries near the main diagonal.
Since the number of nonzero elements in a sparse matrix is much lesser
than the number of zero entries, it is advantageous to make
use of this property of the matrix to reduce the storage space required for the
matrix and also reduce the computational work required to solve systems
involving sparse matrices. Profile reducing algorithms like the one presented
in this paper try to reduce the profile by making a symmetric
permutation of rows and columns. The exchange method developed
in this paper, makes a series of permutations in
an initial ordering to strictly improve the profile.