Fast sparse matrix multiplication
A new space-efficient representation for sparse matrices is introduced and a fast sparse matrix multiplication algorithm based on the new representation is presented. The scheme is very efficient when the nonzero elements of a sparse matrix are partially or fully adjacent to one another as in band or triangular matrices. The space complexity of the new representation is better than that of existing algorithms when the number of sets of adjacent nonzero elements, called segments, is less than two thirds of the total number of nonzero elements. The time complexity of the associated sparse matrix multiplication algorithm is also better or even much better than that of existing schemes depending on the number of segments in the factor matrices. © 1992.