this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

Abstract. We present and analyze a subgrid viscosity Lagrange-Galerkin method that combines the subgrid eddy viscosity method proposed in W. Layton, A connection between subgrid scale eddy viscosity and mixed methods. Appl. Math. Comp., 133: 147-157, 2002, and a conventional Lagrange-Galerkin method in the framework of P1⊕ cubic bubble finite elements. This results in an efficient and easy to i...

This paper deals with the design of interpolating wavelets based on a variety of Lagrange functions, combined with novel signal processing techniques for digital imaging. Halfband Lagrange wavelets, B-spline Lagrange wavelets and Gaussian Lagrange (Lagrange distributed approximating functional (DAF)) wavelets are presented as specific examples of the generalized Lagrange wavelets. Our approach ...

This thesis proposes a two-stage optimization for solving unit commitment. In the first stage, Lagrangian Relaxation (LR) method is used to solve unit commitment using a sub-gradient algorithm for updating Lagrange multipliers. In the second stage, Particle Swarm Optimization (PSO) is applied to update Lagrange multipliers in the Lagrangian Relaxation method (PSOLR). Lagrange multipliers soluti...

In this paper, cross entropy method is used for solving dual Lagrange support vector machine (SVM). Cross entropy (CE) method is a new practical approach which is widely used in some applications such as combinatorial optimization, learning algorithm and simulation. Our approach refers to Kernel Adatron which is solving dual Lagrange SVM using gradient ascent method. Hereby, the cross entropy m...

A novel relaxation labeling (RL) algorithm is proposed. RL is posed as a constrained optimization problem and the solution is found by using the Lagrangian multiplier method and a technique used in the graded Hoppeld neural network. In terms of the optimized objective value, the algorithm performs almost as well as simulated annealing, as shown by the experimental results. Also, the resulting a...

The problem of investing y (0) dollars at time 0 to duplicate a contingent claim is formulated as a dynamic optimization problem and solved by the Lagrange method. As an example, the well-known formula of Black and Scholes on option pricing is derived. If the function defining dy (t) is concave in y (t), owing to costs of trading in incomplete markets, there is economy of scale in producing man...

The Lagrange multiplier method of Babuska for the approximate solution of Dirichlet's problem for second order elliptic equations is reformulated. Based on this formulation, new estimates for the error in the solution and the boundary flux are given. Efficient methods for the solution of the approximate problem are discussed.

A novel relaxation labeling (RL) method is presented based on Augmented Lagrangian multipliers and the graded Hoppeld neural network (ALH). In this method, an RL problem is converted into a constrained optimization problem and solved by using the augmented Lagrangian and Hoppeld techniques. The ALH method yields results comparable to the best of the existing RL algorithms in terms of the optimi...

In this paper, an analysis of 3-dimensional problem using a fictitious domain method based on distributed Lagrange multiplier is discussed. Using this approach allows us to compute moving boundary problems successfully. First of all, how to use a fictitious domain method using navier stokes equations is explained. Next, incompressible viscous fluid around circular cylinder and ball are restrict...