Global Krylov subspace methods are the most efficient and robust methods to solve generalized coupled Sylvester matrix equation. In this paper, we propose the nested splitting conjugate gradient process for solving this equation. This method has inner and outer iterations, which employs the generalized conjugate gradient method as an inner iteration to approximate each outer iterate, while each...

K e y w o r d s R o s e n b r o c k methods, A-stable, Parallel algorithm, Stiff initial value problem, Adal> tivity. 1. I N T R O D U C T I O N We consider the numerical solution of systems of initial value ordinary differential equations (ODEs), i.e., initial value problems (IVPs), of the form y'(t) -f (y(t)) , y(to) = Yo, (1) where y : R --* R "~ and f : R "~ --* R m. Runge-Kutta methods app...

This paper presents a design of Rectangular Fractal microstrip patch antenna using Iteration Methods by cutting different slots on rectangular microstrip antenna and experimentally studied on IE3D software This design is achieved by using three stages of iteration and a Probe feed This design has been studied in 3 iterations The radiation pattern of the proposed fractal shaped antennas maintain...

In this work we analyze and compare two recent variational models for image denoising and improve their reconstructions by applying a Bregman iteration strategy. One of the standard techniques in image denoising, the ROF-model (cf. Rudin et al. in Physica D 60:259–268, 1992), is well known for recovering sharp edges of a signal or image, but also for producing staircase-like artifacts. In order...

Recently, two families of HSS-based iteration methods are constructed for solving the system of absolute value equations (AVEs), which is a class of non-differentiable NP-hard problems. In this study, we establish the Picard-CSCS iteration method and the nonlinear CSCS-like iteration method for AVEs involving the Toeplitz matrix. Then, we analyze the convergence of the Picard-CSCS iteration met...

This paper considers a special but broad class of convex programming (CP) problems whose feasible region is a simple compact convex set intersected with the inverse image of a closed convex cone under an affine transformation. It studies the computational complexity of quadratic penalty based methods for solving the above class of problems. An iteration of these methods, which is simply an iter...

Iterative solvers in combination with multi-grid have been used extensively to solve large algebraic systems. One of the best known is the Runge-Kutta iteration. Previously [4] we reformulated the Runge-Kutta scheme and established a model of a complete V-cycle which was used to optimize the coefficients of the multi-stage scheme and resulted in a better overall performance. We now look into as...

It is well known that a necessary condition for the Lax-stability of the method of lines is that the eigenvalues of the spatial discretization operator, scaled by the time step k, lie within a distance O(k) of the stability region of the time integration formula as k ~ O. In this paper we show that a necessary and sufficient condition for stability, except for an algebraic factor, is that the e...

Domain decomposition techniques provide a flexible tool for the numerical approximation of partial differential equations. Here, we consider mortar techniques for quadratic finite elements in 3D with different Lagrange multiplier spaces. In particular, we focus on Lagrange multiplier spaces which yield optimal discretization schemes and a locally supported basis for the associated constrained m...

When dealing with quantum many-body systems one is faced with problems growing exponentially in the number of particles to be considered. To overcome this curse of dimensionality one has to consider representation formats which scale only polynomially. Physicists developed concepts like matrix product states (MPS) to represent states of interest and formulated algorithms such as the density mat...