Given a large dense matrix $A^{n \times n}$, that does not fit to the memory (RAM). Is there any fast way to compute the exact Frobenius norm of the matrix or its accurate approximation (perhaps, via sampling with reasonable bounds provided)? What if this matrix is a subtraction of two $n \times n$ matrices: $\| A - B \|_F$, where $A$ is sparse, and B is dense?
Fast computation of Frobenius norm under memory limits
matrices