In this context, the whole sparse matrix is never created explicitly, though the decomposition of the matrix is stored. This approach was mainly used historically, when computers had little memory; in such implementations, only the front is in memory, while the factors in the decomposition are written into files.
In this case, the entire sparse matrix is never created explicitly, but its decomposition is retained. This approach was primarily utilized in the past when computers had limited capacity; in such implementations, only a portion of the matrix is stored in memory, while the remaining factors from the decomposition are written to files.