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 context, the entire sparse matrix is never explicitly formed, although its decomposition is stored. This approach was primarily employed in the past when computers had limited memory; in such implementations, only the front is held in memory, while the factors in the decomposition are written to files.