Linear System Of Asymmetric Sparse Approximate Inverse Condition Of Research

Solving large linear equations is a problem often encountered in scientific andengineering computing, and how to efficiently solve large linear equations is veryimportant. With the increasing scale of equations, it has been difficult to obtain goodresults for the traditional iterative method. In such circumstances, the modern iterativemethod has received a great deal of attention. With more and more wide application ofdistributed processors, the research of preconditioners which can be computed inparallel has become a very valuable research direction. Sparse approximate inversemethod has been receiving a lot of attention because of excellent and natural parallelismin last two decades and has accessed to a lot of development.Sparse approximate inverse method is divided into two categories. One is based onFrobenius norm minimization, the other is based on matrix decomposition. In this paper,some successful algorithms in these two methods are listed and numerical experimentson these successful algorithms have been done to compare and summarize the scope ofapplication and effectiveness.In this paper, a approximate inverse algorithm of renewing sparsity pattern (AIRP)based on Frobenius norm minimization and a parallel algorithm of a precondition withsparsity pattern of A (PPA) are proposed. Then numerical experiments are done tocompare the distribution of eigenvalues and iterative curves. It can be seen that AIRPalgorithm is feasible. It has strong robustness, high precision and good parallelism.Finally numerical experiments are done to compare AIRP and PPA mainly from thedistribution of eigenvalues and iterative curves. And the conclusion is that AIRPpretreatment has higher precision and iteratives faster, but needs longer time onpreprocessing and on the contrary PPA pretreatment has lower precision and iterativesmore slowly but needs shorter time on preprocessing and less storage space.