Abstract A method for computing an approximate inverse preconditioner of a matrix A which all eigenvalues have negative real parts is proposed. The approximate solution of the special Sylvester matrix equation AX+ XA = I, which is an approximate inverse preconditioner of matrix A, is obtaining by the successive approximations method. Some numerical experiments on test matrices from Harwell-Boin...

Introduction: Iterative reconstruction techniques provide better image quality and have the potential for reconstructions with lower imaging dose than classical methods in computed tomography (CT). However, the computational speed is major concern for these iterative techniques. The system matrix calculation during the forward- and back projection is one of the most time- cons...

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....

In this paper we discuss the numerical solution of projected generalized Lyapunov equations using the matrix sign function method. Such equations arise in stability analysis and control problems for descriptor systems including model reduction based on balanced truncation. It is known that the matrix sign function method applied to a matrix pencil λE−A converges if and only if λE−A is of index ...

In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution o...