Open AccessINCOMPLETE CHOLESKY FACTORIZATION IN FIXED MEMORY WITH FLEXIBLE DROP-TOLERANCE STRATEGY
Author(s) -
Sergey Saukh
Publication year - 2014
Publication title -
computing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.184
H-Index - 11
eISSN - 2312-5381
pISSN - 1727-6209
DOI - 10.47839/ijc.2.2.200
Subject(s) - cholesky decomposition , incomplete cholesky factorization , factorization , minimum degree algorithm , incomplete lu factorization , matrix decomposition , matrix (chemical analysis) , factor (programming language) , mathematics , computer science , mathematical optimization , algorithm , physics , materials science , eigenvalues and eigenvectors , quantum mechanics , programming language , composite material
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 t - drop-tolerance strategies, the (m, p) strategy allows to form the factor matrix in fixed memory.