A Comparison of Two Equivalent Real Formulations for Complex-Valued Linear Systems Part 2: Results

Real-Valued Iterative Algorithms for Complex Symmetric Linear Systems

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...

Complex fuzzy linear systems

Comparison Results for Two-dimensional Half-linear Cyclic Differential Systems

Two identities of the Picone type for a class of half-linear differential systems in the plane are established and the Sturmian comparison theory for such systems is developed with the help of these new formulas.

Block preconditioning of real-valued iterative algorithms for complex linear systems

We revisit real-valued preconditioned iterative 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. We argue that if either the real or the symmetric part of the coefficient matrix is positive...

Comparison results on the preconditioned mixed-type splitting iterative method for M-matrix linear systems

Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditio...