*Correspondence: [email protected] 1School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi 710048, China Full list of author information is available at the end of the article Abstract Some convergence conditions on successive over-relaxed (SOR) iterative method and symmetric SOR (SSOR) iterative method are proposed for non-Hermitian positive definite linear systems. Some examples are ...

We consider real-valued preconditioned Krylov subspace methods for the solution of complex linear systems, with an emphasis on symmetric (non-Hermitian) problems. Different choices of the real equivalent formulation are discussed, as well as different types of block preconditioners for Krylov subspace methods. Numerical experiments illustrating the performance of the various approaches are pres...

In this paper, we parallelize a new algorithm for solving non– symmetric Toeplitz linear systems. This algorithm embeds the Toeplitz matrix in a larger structured matrix, then transforms it into an embedded Cauchy–like matrix by means of trigonometric modifications. Finally, the algorithm applies a modified QR transformation to triangularize the augmented matrix. The algorithm combines efficien...

Large sparse non-symmetric linear systems of equations often occur in many scientific and engineering applications. In this paper, we present a comparative study of some preconditioned Krylov iterative methods, namely CGS, Bi-CGSTAB, TFQMR and GMRES for solving such systems. To demonstrate their efficiency, we test and compare the numerical implementations of these methods on five numerical exa...

We present an extension of an update technique for preconditioners for sequences of non-symmetric linear systems that was proposed in [5]. In addition, we describe an idea to improve the implementation of the update technique. We demonstrate the superiority of the new approaches in numerical experiments with a model problem.

We introduce a uniformly convergent iterative method for the systems arising from non-symmetric IIPG linear approximations of second order elliptic problems. The method can be viewed as a block Gauß–Seidel method in which the blocks correspond to restrictions of the IIPG method to suitably constructed subspaces. Numerical tests are included, showing the uniform convergence of the iterative meth...

We present a new approach to preconditioning for very large, sparse, non-symmetric, linear systems. We explicitly compute an approximate inverse to our original matrix that can be applied most efficiently for iterative methods on massively parallel machines. The algorithm and its implementation on the Connection Machine CM-2 are discussed in detail and supported by timings obtained from real pr...