newton raphson method

We propose an algorithm that estimates the real roots of differentiable functions on closed intervals. Then, we extend this algorithm to real differentiable functions that are dominated by a polynomial. For each starting point, our method converges to the nearest root to the right or left hand side of that point. Our algorithm can look for missed roots as well and theoretically it misses no root. Furthermore, we do not find the roots by randomly chosen initial guesses. The iterated sequences in our algorithms converge linearly. Therefore, the rate of convergence can be accelerated considerably to make it comparable to Newton-Raphson and other high-speed methods. We have illustrated our algorithms with some concrete examples. Finally, the pseudo-codes of the related algorithms are presented at the end of this manuscript.

We study the convergence of the Krasnoselskii sequence $x_{n+1}=\frac{x_n+g(x_n)}{2}$ for non-self mappings on closed intervals. We show that if $g$ satisfies $g^{'}\ge -1$ along with some other conditions, this sequence converges to a fixed point of $g$. We extend this fixed-point result to a novel and efficient root-finding method. We present concrete examples at the end. In these examples, we make a comparison between Newton-Raphson and our method. These examples also reveal how our method can be applied efficiently to find the fixed points of a real-valued function.

Identifying the structures of dependence between financial assets is one of the interesting topics to researchers. However, there are challenges to this purpose. One of them is the modelling of heavy tail distributions. Distributions of financial assets generally have heavier tails than other distributions, such as exponential distributions. Also, the dependence of financial assets in crashes is stronger than in booms and consequently the skewed parameter in the left tail is more.To address these challenges, there is a function called Copula. So, copula functions are suggested for modelling dependency structure between multivariate data without any assumptions on marginal distributions, which they solve the problems of dependency measures such as linear correlation coefficient. Also, tail dependency measures have analytical formulas with copula functions. In general, the copula function connects the joint distribution functions to the marginal distribution of every variables.With regard, we have introduced a factor copula model that is useful for models where variables are based on latent factor structures. Finally, we have estimated the parameters of factor copula by Simulated method of Moment, Newton-Raphson method and Robbins-Monroe algorithm and have compared the results of these methods to each other.

The initial attached cell layer in multispecies biofilm growth is studied in this paper. The corresponding mathematical model leads to discuss a free boundary problem for a system of nonlinear hyperbolic partial differential equations, where the initial biofilm thickness is equal to zero. No assumptions on initial conditions for biomass concentrations and biofilm thickness are required. The data that the problem needs are the concentration of biomass in the bulk liquid and biomass flux from the bulk liquid. The differential equations are converted into an equivalent system of Volterra integral equations. We use Newton-Raphson method to solve the nonlinear system of Volterra integral equations (SVIEs) of the second kind. This method converts the nonlinear system of integral equations into a linear integral equation at each step.

This is a new lifetime Exponential "distribution using the Topp-Leone generated family of distributions proposed by Rezaei et al. The new distribution is called the Topp-Leone Exponential (TLE) distribution". What is done in this paper is an estimation of the "unlabeled two parameters for Topp-Leone Exponential distribution model by using the maximum likelihood estimator method to get the derivation of the point estimators for all unlabeled parameters according to iterative techniques as Newton $-$ Raphson method, then to derive Ordinary least squares estimator method". "Applying all two methods to estimate related probability functions; death density function, cumulative distribution function, survival function and hazard function (rate function)". When examining the numerical results for probability survival function by employing mean squares error measure and mean absolute percentage measure, this may lead to work on the best method in modeling a set of real data.

A fourth-order and rapid numerical algorithm, utilizing a procedure as Runge–Kutta methods, is derived for solving nonlinear equations. The method proposed in this article has the advantage that it, requiring no calculation of higher derivatives, is faster than the other methods with the same order of convergence. The numerical results obtained using the developed approach are compared to those obtained using some existing iterative methods, and they demonstrate the efficiency of the present approach.

In this paper we investigate in detail the applications of the classical Newton-Raphson method in connection with a space-time finite element discretization scheme for the inviscid Burgers equation in one dimensional space. The underlying discretization method is the so-called streamline diffusion method, which combines good stability properties with high accuracy. The coupled nonlinear algebraic equations thus obtained in each space-time slab are solved by the generalized Newton-Raphson method. Exploiting the band-structured properties of the Jacobian matrix, two different algorithms based on the Newton-Raphson linearization are proposed. In a series of examples, we show that in each time-step a quadratic convergence order is attained when the Newton-Raphson procedure applied to the corresponding system of nonlinear equations.