Many problems in computational sciences rely on the inversion of a sparse, "block-symmetric" matrix. We are all familiar with symmetric matrices in which element A_ij = A_ji. A block-symmetric matrix is one composed of kxk blocks (typically, k=2 or k=3), where each block, B_ij, is identical to block B_ji. By taking advantage of both symmetry and sparseness in a matrix, storage requirements are drastically reduced from that of a full matrix, allowing for larger problems to be handled with less memory.

Since there is no evidence of a solver that takes advantage of both sparseness and block-symmetry, the purpose of this project is to develop and test such a solver. Participants begin by studying traditional solutions for general systems of equations, symmetric systems, and sparse systems. Finally, they synthesise this knowledge to create the desired sparse, block-symmetric solver.