Fuzzy Newton-Cotes method for integration of fuzzy functions that was proposed by Ahmady in [1]. In this paper we construct error estimate of fuzzy Newton-Cotes method such as fuzzy Trapezoidal rule and fuzzy Simpson rule by using Taylor's series. The corresponding error terms are proven by two theorems. We prove that the fuzzy Trapezoidal rule is accurate for fuzzy polynomial of degree one and...

We present an Altered Jacobian Newton Iterative Method for solving nonlinear elliptic problems. Effectiveness of the proposed method is demonstrated through numerical experiments. Comparison of our method with Newton Iterative Method is also presented. Convergence of the Newton Iterative Method is highly sensitive to the initialization or initial guess. Reported numerical work shows the robustn...

in this paper, we present a full newton step feasible interior-pointmethod for circular cone optimization by using euclidean jordanalgebra. the search direction is based on the nesterov-todd scalingscheme, and only full-newton step is used at each iteration.furthermore, we derive the iteration bound that coincides with thecurrently best known iteration bound for small-update methods.

Quasi-Newton methods have played a prominent role, over many years, in the design of effective practical methods for the numerical solution of nonlinear minimization problems and in multi-dimensional zero-finding. There is a wide literature outlining the properties of these methods and illustrating their performance [e.g., [8]]. In addition, most modern optimization libraries house a quasi-Newt...

In this paper, we investigate the convergence behaviour of a class of regularized Newton methods for the solution of nonlinear inverse problems. In order to keep the overall numerical effort as small as possible, we propose to solve the linearized equations by certain semiiterative regularization methods, in particular, iterations with optimal speed of convergence. Our convergence rate analysis...

The paper deals with three different Newton algorithms that have recently been worked out in the general frame of affine invariance. Of particular interest is their performance in the numerical solution of discretized boundary value problems (BVPs) for nonlinear partial differential equations (PDEs). Exact Newton methods, where the arising linear systems are solved by direct elimination, and in...

Full Waveform Inversion (FWI) methods use generally gradient based method, such as the nonlinear conjugate gradient method or more recently the l-BFGS quasi-Newton method. Several authors have already investigated the possibility of accounting more accurately for the inverse Hessian operator in the minimization scheme through Gauss-Newton or exact Newton algorithms. We propose a general framewo...