Incomplete Cholesky factorization in fixed memory with flexible drop-tolerance strategy

We propose an incomplete Cholesky factorization for the solution of large positive definite systems of equations and for the solution of large-scale trust region sub-problems. The factorization is based on the two-parameter (m,p)-drop-tolerance strategy for insignificant elements in the incomplete factor matrix. The factorization proposed essentially reduces the negative processes of irregular distribution and accumulation of errors in factor matrix and provides the optimal rate of memory filling with essential nonzero elements. On the contrary to the known p-retain and tau-drop-tolerance strategies, the (m,p)-strategy allows to form the factor matrix in fixed memory