The connection between closed Newton-Cotes, trigonometrically-fitted differential methods and symplectic integrators is investigated in this paper. It is known from the literature that several one step symplectic integrators have been obtained based on symplectic geometry. However, the investigation of multistep symplectic integrators is very poor. Zhu et al. (1996) presented the well known ope...

Quasi-Newton methods have been utilized as a standard technique for solving nonlinear optimization problems and nonlinear systems of equations for over thirty years. These methods, in almost all cases, make use of data obtained from the step just completed in the variable space to revise the current approximation to the Hessian / Jacobian. Recently, a new class of multi-step quasi-Newton method...

In this paper, we present a new family of two-step Newton-type iterative methods with memory for solving nonlinear equations. In order to obtain a Newton-type method with memory, we first present an optimal two-parameter fourth-order Newton-type method without memory. Then, based on the two-parameter method without memory, we present a new two-parameter Newton-type method with memory. Using two...

Recently, we have extended SDP by adding a quadratic term in the objective function and give a potential reduction algorithm using NT directions. This paper presents a predictor-corrector algorithm using both Dikin-type and Newton centering steps and studies properties of Dikin-type step. In this algorithm, when the condition K(XS) is less than a given number K0, we use Dikin-type step. Otherwi...

This paper establishes the higher-order equivalence of the k-step bootstrap, introduced recently by Davidson and MacKinnon (1999), and the standard bootstrap. The k-step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper also ...

1 This paper establishes the higher-order equivalence of the k-step bootstrap, introduced recently by Davidson and MacKinnon (1999), and the standard bootstrap. The k-step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper als...

Many problems in image processing are addressed via the minimization of a cost functional. The most prominent optimization technique is the gradient descent, often used due to its simplicity and applicability where other techniques, e.g., those coming from discrete optimization, can not be used. Yet, gradient descent suffers from a slow convergence, and often to just local minima which highly d...

In this article we present robust, efficient and accurate fully implicit time-stepping schemes and nonlinear solvers for systems of reaction-diffusion equations. The applications of reaction-diffusion systems is abundant in the literature, from modelling pattern formation in developmental biology to cancer research, wound healing, tissue and bone regeneration and cell motility. Therefore, it is...

We are concerned with the reconstruction of a sound-soft obstacle using far field measurements of scattered waves associated with incident plane waves sent from one incident direction but at multiple frequencies. We define, at each frequency, observable shapes as the ones which are described by finitely many modes and produce far field patterns close to the measured one. Our analysis consists o...

One of the widely used methods for solving a nonlinear system of equations is the quasi-Newton method. The basic idea underlining this type of method is to approximate the solution of Newton's equation by means of approximating the Jacobian matrix via quasi-Newton update. Application of quasi-Newton methods for large scale problems requires, in principle, vast computational resource to form and...