A lot is known about the forward iterates of an analytic function which is bounded by 1 in modulus on the unit disk D. The Denjoy-Wolff Theorem describes their convergence properties and several authors, from the 1880’s to the 1980’s, have provided conjugations which yield very precise descriptions of the dynamics. Backward-iteration sequences are of a different nature because a point could hav...

in this paper, we apply the local fractional adomian decomposition and variational iteration methods to obtain the analytic approximate solutions of fredholm integral equations of the second kind within local fractional derivative operators. the iteration procedure is based on local fractional derivative. the obtained results reveal that the proposed methods are very efficient and simple tools ...

In this paper, we first show that the iteration {xn} defined by xn+1 = P ((1−αn)xn +αnTP [βnTxn + (1− βn)xn]) converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with err...

Initial Semantics aims at interpreting the syntax associated to a signature as the initial object of some category of “models”, yielding induction and recursion principles for abstract syntax. Zsidó [Zsi10, Chap. 6] proves an initiality result for simply–typed syntax: given a signature S, the abstract syntax associated to S constitutes the initial object in a category of models of S in monads. ...

General idea of nonlinear correcting factors that was successfully applied to accelerate and derive algorithms for many linear and nonlinear problems is used to develop several efficient procedures for solving linear systems of equations based on the Jacobi algorithm. Results of the theoretical study and extensive computer experiments for stochastic matrices are presented and analyzed to determ...

A grove theory is a Lawvere algebraic theory T for which each hom-set T (n, p) is a commutative monoid; composition on the right distrbutes over all finite sums: ( ∑ i∈F fi) ·h = ∑ i∈F fi ·h. A matrix theory is a grove theory in which composition on the left and right distributes over finite sums. A matrix theory M is isomorphic to a theory of all matrices over the semiring S = M(1, 1). Example...

We consider an online optimization problem on a compact subset S ⊂ R (not necessarily convex), in which a decision maker chooses, at each iteration t, a probability distribution x over S, and seeks to minimize a cumulative expected loss, ∑T t=1 Es∼x(t) [`(s)], where ` is a Lipschitz loss function revealed at the end of iteration t. Building on previous work, we propose a generalized Hedge algor...

This paper considers feasible long-step primal-dual path-following methods for semidefinite programming based on Newton directions associated with central path equations of the form Φ(PXP T , P−T SP−1) − νI = 0, where the map Φ and the nonsingular matrix P satisfy several key properties. An iteration-complexity bound for the long-step method is derived in terms of an upper bound on a certain sc...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.