Solving Complex-Valued Linear Systems via Equivalent Real Formulations

Algebraic Solving of Complex Interval Linear Systems by Limiting ‎Factors‎

In this work, we propose a simple method for obtaining the algebraic solution of a complex interval linear system where coefficient matrix is a complex matrix and the right-hand-side vector is a complex interval vector. We first use a complex interval version of the Doolittle decomposition method and then we restrict the Doolittle's solution, by complex limiting factors, to achieve a complex in...

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...

Solving Real Linear Systems with the Complex Schur Decomposition

If the complex Schur decomposition is used to solve a real linear system, then the computed solution generally has a complex component because of roundoff error. We show that the real part of the computed solution that is obtained in this way solves a nearby real linear system. Thus, it is “numerically safe” to obtain real solutions to real linear systems via the complex Schur decomposition. Th...

Complex fuzzy linear systems

On Solving Pentadiagonal Linear Systems via Transformations

Many authors studied numeric algorithms for solving the linear systems of the pentadiagonal type. The well-known Fast Pentadiagonal System Solver algorithm is an example of such algorithms. The current article is describes new numeric and symbolic algorithms for solving pentadiagonal linear systems via transformations. New algorithms are natural generalization of the work presented in [Moawwad ...