In this paper , we study the strong convergence of SP iterative scheme for quasi-contractive operators in Banach spaces. We show that Picard , Mann , Ishikawa , Noor, new two step and SP iterative schemes are equivalent for quasi-contractive operators. In addition, we show that the rate of convergence of SP iterative scheme is better than the other iterative schemes mentioned above for increasi...

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we prove that, given a such variety X which is not exceptional, then X is smooth if and only if an appropriate toric variety contained in X is smooth. keywords:...

Let X, ‖ · ‖ be a Banach space and T a self-map of X. Let xn 1 f T, xn be some iteration procedure. Suppose that F T , the fixed point set of T , is nonempty and that xn converges to a point q ∈ F T . Let {yn} ⊆ X and define n ‖yn 1 − f T, yn ‖. If lim n 0 implies that limyn q, then the iteration procedure xn 1 f T, xn is said to be T -stable. Without loss of generality, we may assume that {yn}...

We present a method based on Picard’s idea to construct a sequence of controls and a sequence of solutions of linearized systems such that their limits form a solution to the control problem. By doing this, we simplified the works in the references, and deduced the controllability for semilinear coupled parabolic systems.

Numerical formulations of density functional theories for inhomogeneous fluids (Fluid-DFTs) require the solution of large systems of equations with many degrees of freedom (DOFs) per node on a computational grid. Historically solvers for these problems have used simple Picard iterations across DOFs or, more recently, fully-coupled general algebraic techniques. In this paper we look at Fluid-DFT...

We present a parallel algorithm for solving backward stochastic differential equations. We improve the algorithm proposed in Gobet and Labart (2010), based on an adaptive Monte Carlo method with Picard’s iterations, and propose a parallel version of it. We test our algorithm on linear and non linear drivers up to dimension 8 on a cluster of 312 CPUs. We obtained very encouraging efficiency rati...

In this paper we devise a method for recovering band limited signals which have been subjected to a distorting procedure called companding. A band limited signal is a function in L2 whose Fourier transform vanishes outside of a bounded interval. In practice most real signals are in this class since they have no indefinitely high frequency components. The operation of companding a signal f(t) co...

We consider the boundary value problem:    x (m) (t) = f (t, x(t)), a ≤ t ≤ b, m > 1 x(a) = β 0 ∆x (k) ≡ x (k) (b) − x (k) (a) = β k+1 , continuous at least in the interior of the domain of interest. We give a constructive proof of the existence and uniqueness of the solution, under certain conditions, by Picard's iteration. Moreover Newton's iteration method is considered for the numerical ...

This article presents a theory of modules with iterative connection. This theory is a generalisation of the theory of modules with connection in characteristic zero to modules over rings of arbitrary characteristic. We show that these modules with iterative connection (and also the modules with integrable iterative connection) form a Tannakian category, assuming some nice properties for the und...

We consider some integral equations with iterations of linear modification of the argument which provide us Picard operators and weakly Picard operators. We study the existence, existence and uniqueness, and data dependence for the solutions of these equations. AMS Mathematics Subject Classification (2000): 34K05, 47H10