| In engineering and natural science areas, a lot of problem’s solving involveworking out linear equations. Symmetric indefinite linear systems，which have veryspecial structures are precisely very important in these equations. In scientificcomputation, when the coefficient matrices are symmetric but indefinite, if we simplyrely on direct solutions, ordinary iterative methods or general factorizations, it’s verydifficult to satisfy the accuracy, stability and speed at the same time. Therefore,exploring the effective solution to this specific type of problem is particularly important.The purpose of this essay is to find a good method to solve symmetric indefinitelinear system Ax band it should satisfy the convergence and memory requirements atthe same time.What’s more，it also should make the whole solving process morequickly.This essay first introduces some graph theories and basic knowledge related tosolving linear equations.And it shows how to effectively apply maximum weightedmatching to symmetric indefinite mtrix,including how to split the cycles of matchingand symmetric preordering based on maximum weighted matching which is used topermute A to form2×2diagonal blocks.Then,the paper uses1×1and2×2blockpivoting method to make incompleteLDLT factorization of the coefficient matrix. Atlast, relevant softwares are used to do the numerical experiments in the text, and theyare compared to other methods at advantages and disadvantages. |
