a new meta-heuristic method, based on neuronal communication (nc), is introduced in this article. the neuronal communication illustrates how data is exchanged between neurons in neural system. actually, this pattern works efficiently in the nature. the present paper shows it is the same to find the global minimum. in addition, since few numbers of neurons participate in each step of the method,...

Consider a system of linear algebraic equations with a nonsingular n by n matrix A. When solving this system with GMRES, the relative residual norm at the step k is bounded from above by the so called ideal GMRES approximation. This bound is sharp (it is attainable by the relative GMRES residual norm) in case of a normal matrix A, but it need not characterize the worstcase GMRES behavior if A i...

The GMRES method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix. GMRES-type methods also have been applied to the solution of linear discrete ill-posed problems. Computational experience indicates that for the latter problems variants of the standard GMRES method, that require the solution to live in the range ...

Based on the general inner-outer (GIO) iteration method [5,34] and framework [6], we present a multi-step matrix splitting (GMMS) for computing PageRank, analyze its overall convergence property. Moreover, same idea can be used as preconditioning technique accelerating Krylov subspace methods, such GMRES method. Finally, several numerical examples are given to illustrate effectiveness of propos...

Additive Schwarz preconditioned GMRES is a powerful method for solving large sparse linear systems of equations on parallel computers. The algorithm is often implemented in the Euclidean norm, or the discrete l norm, however, the optimal convergence theory is available only in the energy norm (or the equivalent Sobolev H norm). Very little progress has been made in the theoretical understanding...

We develop an algorithm for computing a sparse approximate inverse for a nonsymmetric positive definite matrix based upon the FFAPINV algorithm. The sparse approximate inverse is computed in the factored form and used to work with some Krylov subspace methods. The preconditioner is breakdown free and, when used in conjunction with Krylovsubspace-based iterative solvers such as the GMRES algorit...

In this paper, we present a block version of incomplete LU preconditioner which is computed as the by-product of block A-biconjugation process. The pivot entries of this block preconditioner are one by one or two by two blocks. The L and U factors of this block preconditioner are computed separately. The block pivot selection of this preconditioner is inherited from one of the block versions of...