A note on simultaneous preconditioning and symmetrization of non-symmetric linear systems.
The paper describes a technique for simultaneous preconditioning and symmetrization for solving large, sparse and non-symmetric problems by CG, MINRES or SYMMLQ. The approach is based on the theory of self-duality. The paper states that sometimes it is beneficial to replace the original problem \(Ax = b\) with non-symmetric matrix \(A\) by \(A^TMAx = A^TMb\). It is shown how to choose the matrix \(M\) in order to get a good numerical scheme for solving the original problem. The efficiency of the introduced approach is illustrated on several numerical examples. Results are compared on several iterative methods.
scientific article; zbMATH DE number 6043443