Is it possible to perform calculations with sparse matrix without any stored elements

I have a matrix that is sparse but still has tons of non-zero elements, all of which are very fast to calculate. Does it make sense, and if yes it is possible, to perform calculations with this matrix without storage of even the non-zero elements?

Answer 1

[John D'Errico]

MATLAB does not allow a sparse matrix of that type, where the un-stored elements are other than zero.

So, no you cannot do any calculations with a matrix in a form that does not exist.