Pursuing a many‐nucleon description of collective rotations of nuclei demands that very large sparse matrix representations of hamiltonians be constructed and diagonalized. Two general computational methods are presented for reducing the computer resources required for these processes. Specifically, a space and time optimal numerical database called a Weighted Search Tree that minimizes the number of redundant intermediate calculations required when calculating the matrix elements of the sparse hamiltonian matrices is given, and a matrix multiplication algorithm for a new space optimal optimal representation for sparse matrices is given which is expected to dramatically decrease the cost of diagonalizing large sparse band matrices. Both methods can be implemented in a broad range of large‐scale scientific applications.