A Parameterized Block Sort Pretreatment Method Based On The Figure

The core of numerical algebra research is to make use of computers to solve allkinds of numerical value with high speed and efficiency. When people deal with thescientific engineering calculation, we often transform the numerical simulation into oneor a series of large linear system due to the complexity of the system. However, with thedevelopment requirements of science and engineering and technology progress, thescale of the problem is gradually increasing, which leads to the augment of unknownnumbers of the corresponding linear system. Therefore, solving the large linear systembecomes one of the most important problems. We study the rapid and efficient solutionof the large-scale linear equations, not only has the theoretical significance but alsocontains actual value.For getting the final solution easily, it is necessary to preconditioning first. Theessence of preconditioning is to switch the large linear system Ax=bin order to getanother equivalent system so that the new system has optimized structureis and easy tosolve.This essay combines the bipartite matching algorithms with the parametric blockordering algorithms, and constrct some precondioners for sparse matrixs effectively. Atfirst, we use the bipartie matching algorithm to reorder the matrices, and scale them tomake it to be the diagonally dominant matrix. After that we use parametric blockordering method and change some different block strategies to solve these system.finally, we make the numerical experiments compare to the results.