Ilut And Minimum Degree Algorithm Application In The Large-scale System Of Linear Equations To Solve

Scientific computing is an important topic used for solving large linear equations,and the large sparse matrices take up a large proportion in practical applications,Therefore solving the large sparse linear equations efficiently has become one of ourmain research directions. The incomplete decomposition preconditioner attaches ourattention, not only because it is able to maintain the sparsity of the linear system but itcan also reduce storage complexity and the amount of calculation. This paper studies theperformance algorithm to solve linear sparse system and construct a valid incompletedecomposition preconditioner.Firstly, it is introduced that the classic iterative method, preconditioning techniqueand incomplete decomposition. Furthermore, the MILUT algorithm can be gettingjust from improving the existed incomplete decomposing and preconditioning algorithmILUT. Finally, the MDILUTP algorithm can be concluded with the methodof minimum degree recording. It is obvious that the algorithms have good results for thedecomposition of sparse matrice through numerical experiments.In order to ensure that the sparse nature of matrices is not destroyed after thedecomposition, non-zero elements of the controlling parameters are usually set toconstruct preconditions of decomposing symmetric positive matrices or the generalmatrices. In general, constructing reasonable non-zero elements of controllingparameters has achieved a certain effect to get the improved incomplete decompositionpreconditioner.For non-symmetric matrices, based on ILUTP pretreatment technology andthe method of minimum degree recording, the nonzero weight parameters are added inthe process of pivoting to reduce the generated elements during process of thereordering matrices decomposition.Thereby the complexity of storage and computationis reduced, the operational efficiency is improved and the sparsity nature of the matricesis ensured not to be destroyed in the decomposition process.