A submatrix algorithm for the matrix-vector multiplication of very large matrices

In self-consistent field (SCF) calculations the construction of the Fock matrix is most time-consuming step. The Fock matrix construction may formally be seen as a matrix-vector multiplication, where the matrix is the supermatrix,??_ijkl, and the vector is the first-order density matrix, γ_ij. This formalism should be optimal for vector machines. This is not, however, fully utilized in most programs running on computers with small core memory. The size of the ?? matrix, typically in the order of 10⁶–10⁸ elements, has forced programmers to implement other nonvectorizable methods. We will present a submatrixbased algorithm which will partition the supermatrix so that vectorizable methods can be employed. The method will also reduce the input/output.