This paper presents equivalent forms of the Sylvester matrix equations. These equivalent forms allow us to use block linear methods for solving large Sylvester matrix equations. In each step of theses iterative methods we use global FOM or global GMRES algorithm for solving an auxiliary block matrix equations. Also, some numerical experiments for obtaining the numerical approximated solution of...

In this paper we discuss the effects of the communication latency upon the dynamic load balance for computations which require global synChronization are discussed. Experimental results from the study of the performance of iteration methods on an NCUBE 1 are presented.

Transmission eigenvalues have important applications in inverse scattering theory. They can be used to obtain useful information of the physical properties, such as the index of refraction, of the scattering target. Despite considerable effort devoted to the existence and estimation for the transmission eigenvalues, the numerical treatment is limited. Since the problem is non-standard, classica...

This chapter contains an overview of some of the important techniques used to solve linear systems of equations Ax = b (1) by iterative methods. We consider methods based on two general ideas, splittings of the coeecient matrix, leading to stationary iterative methods, and Krylov subspace methods. These two ideas can also be combined to produce preconditioned iterative methods. In addition, we ...

Preconditioned iterative methods are described for the solution of an elliptic partial differential equation over an unit square region with Robbins boundary conditions. Transform based preconditioners are constructed and analyzed. The motivation is to exploit the fast inversion of transform based systems via the fast transform. We prove that transform based preconditioners can be chosen so tha...

In many applications we have to solve a linear system Ax = b with A ∈ Rn×n and b ∈ Rn given. If n is large the solution of the linear system takes a lot of operations, and standard Gaussian elimination may take too long. But in many cases most entries of the matrix A are zero and A is a so-called sparse matrix. This means each equation only couples very few of the n unknowns x1, . . . , xn. A t...

For many elliptic PDE problems, finite-difference and finite-element methods are the techniques of choice. In a finite-difference approach, a solution uk on a set of discrete gridpoints 1, . . . , k is searched for. The discretized partial differential equation and boundary conditions create linear relationships between the different values of uk. In the finite-element method, the solution is e...

This tutorial paper discusses the use of iterative restoration algorithms for the removal of linear blurs from photographic Images which may also be assumed to be degraded by pointwise nonlineariries such as film saturation and additive noise. lterative algorithms are particularly attractive for this application because they allow for the incorporation of various types of prior knowledge about ...