In summary, the ML classification approaches are quantitatively accurate for the H-matrices examined here by training on just 1% of the elements with a major reduction on the number of predicted non-negligible elements to be calculated. For the largest examples, 4-mode vinyl with the saddle point basis and 10-mode glycine the reductions are around 90%. Also the results here show that the percentage reduction increases with the number of modes. Note the matrices considered here were not so large as to need special routines that can exploit sparse matrices. However, there are routines that do exploit this sparsity, both in terms of greatly reducing the memory needed to store the non-zero elements and also to obtain eigenvalues. Examples are scipy.sparse.linalg in Numpy and sparse solver routines in the MKL library. Also, iterative routines that multiply the H-matrix by a trial vector clearly benefit from sparsity.