We consider certain speed estimates for Krylov subspace methods (such as GMRES) when applied upon systems consisting of a compact operator K with small unstructured perturbation B. Information about the decay of singular values of K is also assumed. Our main result is that the Krylov method will perform initially at superlinear speed when applied upon such pre-conditioned system. However, with ...

Dengue is a complex disease because of the link it forms between humans, mosquitoes, and several virus serotypes, including efficient strategies for vector survival strategies. For this reason, the understanding of various factors that influence the recurrence of Dengue has been an inescapable fight for policy makers and scientists alike. In this paper, the susceptible-infected-recovered (SIR) ...

The random perturbation of generalized reduced gradient method for optimization under nonlinear differentiable constraints is proposed. Generally speaking, a particular iteration of this method proceeds in two phases. In the Restoration Phase, feasibility is restored by means of the resolution of an auxiliary nonlinear problem, a generally nonlinear system of equations. In the Optimization Phas...

Assume that F is a nonlinear operator which is Lipschitzian and stronglymonotone on a nonempty closed convex subset C of a real Hilbert space H. Assume also thatΩ is the intersection of the fixed point sets of a finite number of Lipschitzian pseudocontractive self-mappings on C. By combining hybrid steepest-descent method, Mann’s iteration method and projection method, we devise a hybrid iterat...

We show that recent applications of the homotopy perturbation method the Adomian decomposition method and the variational iteration method are completely useless for the treatment of nonlinear problems.

Based on He's variational iteration method idea, we modified the fractional variational iteration method and applied it to construct some approximate solutions of the generalized time-space fractional Schrödinger equation (GFNLS). The fractional derivatives are described in the sense of Caputo. With the help of symbolic computation, some approximate solutions and their iterative structure of th...

A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...

In the present study, natural transform iterative method (NTIM) has been implemented for solution of a fractional Zakharavo–Kuznetsov (FZK) equation. NTIM is relatively new technique handling non-linear differential equations. The tested upon two FZK equalities. proposed compared with existing perturbation–iteration algorithm (PIA) and residual power series (RPSM). From numerical results, it cl...

In this paper, we will use a modified  variational iteration method (MVIM) for solving an inverse heat conduction problem (IHCP). The approximation of the temperature and the heat flux at  are considered. This method is based on the use of Lagrange multipliers for the identification of optimal values of parameters in a functional in Euclidian space. Applying this technique, a rapid convergent s...

Motivated by variational models in continuum mechanics, we introduce a novel algorithm for performing nonsmooth and nonconvex minimizations with linear constraints. We show how this algorithm is actually a natural generalization of well-known non-stationary augmented Lagrangian methods for convex optimization. The relevant features of this approach are its applicability to a large variety of no...