The (Extrapolated) Alternating Direction Implicit Preconditioners for the class of Conjugate Gradient Methods are applied for the solution of the second order elliptic equation in a rectangle under Dirichlet boundary conditions. The PDE is approximated by uniform meshes of 5− and 9−point difference schemes and analytic expressions for the optimal acceleration and extrapolation parameters are ob...

We consider the gradient method xt+1 = xt + γt(st + wt), where st is a descent direction of a function f : �n → � and wt is a deterministic or stochastic error. We assume that ∇f is Lipschitz continuous, that the stepsize γt diminishes to 0, and that st and wt satisfy standard conditions. We show that either f(xt) → −∞ or f(xt) converges to a finite value and ∇f(xt) → 0 (with probability 1 in t...

We consider new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with cross derivative terms. Our approach is based on the unconditionally stable ADI scheme proposed by Hundsdorfer [12]. Different numerical discretizations which lead to schemes which are fourth-order accurate in space and sec...

sex in evolution Adi Livnat∗† ‡, Christos Papadimitriou ‡ , Jonathan Dushoff § and Marcus W. Feldman ¶ †Miller Institute for Basic Research in Science, University of California, Berkeley, CA 94720 USA,‡Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720 USA,§Department of Biology, McMaster University, Hamilton, ON L8S 4K1 CANADA, and ¶Departme...

A Lagrange multiplier and Hopfield-type barrier function method is proposed for approximating a solution of the traveling salesman problem. The method is derived from applications of Lagrange multipliers and a Hopfield-type barrier function and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier par...

This paper presents a novel approach to recognize Grantha, an ancient script in South India and converting it to Malayalam, a prevalent language in South India using online character recognition mechanism. The motivation behind this work owes its credit to (i) developing a mechanism to recognize Grantha script in this modern world and (ii) affirming the strong connection among Grantha and Malay...

To simplify the problem of estimating the motion parameters, in this paper, based on the properties of human motion perception we present a feasible approach, which can estimate the motion direction and the motion extension for a linear motion blurred image. Two main parts are developed in our approach. Hough transform is first used to detect the angle (i.e., motion direction) of a given linear...