Sparse matrix storage formats and acceleration of iterative solution of linear algebraic systems with dense matrices

In the paper, formulas for comparing sparse matrix storage formats are derived. An iterative algorithm for solving linear algebraic systems using the sparse row format for storing prefiltered preconditioners is designed. A modification of the sparse row format leading to 1.14–1.23 times speed-up for matrices of order 1000 is suggested. It is demonstrated that as opposed to the usual storage format, the sparse row format provides for 1.5–1.6 times speed-up in solving linear systems of orders 4800, 6000, and 8000. The use of the results obtained allows one to reduce both memory and time requirements in solving large-scale problems with dense matrices.