‎in this paper‎, ‎we propose two preconditioned aor iterative methods to solve systems of linear equations whose coefficient matrices are z-matrix‎. ‎these methods can be considered as improvements of two previously presented ones in the literature‎. ‎finally some numerical experiments are given to show the effectiveness of the proposed preconditioners‎.‎

lsmr (least squares minimal residual) is an iterative method for the solution of the linear system of equations and leastsquares problems. this paper presents a block version of the lsmr algorithm for solving linear systems with multiple right-hand sides. the new algorithm is based on the block bidiagonalization and derived by minimizing the frobenius norm of the resid ual matrix of normal equa...

in this paper, genetic algorithms (gas) are employed to control simultaneous linear systems in both state and output feedback. first, the similarity transformation is applied to obtain parameterized controllers. this requires solution of a system of equations and also some non-linear inequalities. gas are used to solve these equations and inequalities. therefore, the paper presents an analytica...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

encryption is an important tool for managing and protecting information. cryptography is the only practical means of sending information over an insecure channel. these channels may be computers, telephone lines, satellite, etc. the increasing use of electronic means of data transfer from one point to another, coupled with the growth in networking and internet communication, has extended the ne...

Given free modules $M\subseteq L$ of finite rank $f\geq 1$ over a principal ideal domain $R$, we give procedure to construct basis $L$ from $M$ assuming the invariant factors or elementary divisors $L/M$ are known. matrix $A\in M_{m,n}(R)$ $r$, its nullspace in $R^n$ is $R$-module $f=n-r$. We submodule $f$ naturally associated with $A$ and whose easily computable, determine quotient module then...

In this article, a numerical method based on  improvement of block-pulse functions (IBPFs) is discussed for solving the system of linear Volterra and Fredholm integral equations. By using IBPFs and their operational matrix of integration, such systems can be reduced to a linear system of algebraic equations. An efficient error estimation and associated theorems for the proposed method are also ...