If the coefficient matrix is sparse, large-scale linear systems of the form can be most efficiently solved if the zero elements of are not stored. Sparse storage schemes allocate contiguous storage in memory for the nonzero elements of the matrix, and perhaps a limited number of zeros. This, of course, requires a scheme for knowing where the elements fit into the full matrix.
There are many methods for storing the data (see for instance Saad  and Eijkhout ). Here we will discuss Compressed Row and Column Storage, Block Compressed Row Storage, Diagonal Storage, Jagged Diagonal Storage, and Skyline Storage.