Famili Metode Iterasi Berorde Tiga Untuk Menyelesaikan Persamaan Nonlinear

We discuss a family of iterative methods derived by giving a weight function recur-sively to the corrector of Newton's method, which is a review of article of Herceg and Herceg publised on [Applied Mathematics and Computation, 87 (2010), 2533–2541]. Weighting with a specific index produces Super-Halley's method. Analytically it is shown that the order of the convergence of the method is three. Furthermore, this iteration method requires four function evaluations per iteration, so its efficiency index is 1.316. Then, computational tests show that the discussed method is better than Newton's method, and does not have significant differences with Super Halley's method in terms of error produced

Review Essay: Janet Halley, Split Decisions: How and Why to Take a Break from Feminism

[Excerpt] “My overarching reaction to Janet Halley\u27s recent book, Split Decisions: How and Why to Take a Break from Feminism, can be summarized with a one sentence cliché: The perfect is the enemy of the good.\u27 She holds feminism to a standard of perfection no human endeavor could possibly meet, and then heartily criticizes it for falling short. Though Halley\u27s myriad observations about feminism occasionally resonated with my own views and experiences, ultimately I remain unconvinced that taking a break from feminism would, for me, be either justified or productive. But I did (mostly) enjoy reading it. Halley is well read, cleverly provocative, and a gifted writer. Below I give a somewhat glib and superficial overview of the book, and my reactions to it. I explain why I think Halley is too hard on feminists generally, and on Catharine MacKinnon specifically. And I take her to task for being harshly critical of feminism without offering realistic, pragmatic, or lawyerly alternatives. You can\u27t theorize your way into an abortion, or out of a rape. You can have to rely on a legal system that may fail you, in which case you can work to improve it so that others don\u27t suffer as you did. This is part of the very essence of feminism, which Halley gives short shrift.

Simulation techniques for generalized Gaussian densities

This contribution deals with Monte Carlo simulation of generalized Gaussian random variables. Such a parametric family of distributions has been proposed in many applications in science to describe physical phenomena and in engineering, and it seems also useful in modeling economic and financial data. For values of the shape parameter a within a certain range, the distribution presents heavy tails. In particular, the cases a=1/3 and a=1/2 are considered. For such values of the shape parameter, different simulation methods are assessed.Generalized Gaussian density, heavy tails, transformations of rendom variables, Monte Carlo simulation, Lambert W function

Comparative Analysis of Halley and Hybrid Methods for Numerically Solving the Roots of Non-Linear Equations

Abstract: Finding the roots of nonlinear equations is a fundamental problem in numerical analysis with wide applications in engineering, science, and applied mathematics. The purpose of this study is to conduct a comparative analysis between Halley's method and a selected hybrid method for numerically solving the roots of nonlinear equations. Halley's method is a third-order iterative technique known for its fast convergence when provided with a good initial guess. On the other hand, hybrid methods are designed to combine the strengths of multiple numerical algorithms to enhance accuracy, stability, and robustness against different function characteristics. This study employs four test functions—polynomial, trigonometric, exponential, and logarithmic—to evaluate the performance of both methods in terms of convergence speed, computational efficiency, and sensitivity to initial guesses. The results indicate that Halley's method performs better in terms of speed under ideal conditions, while the hybrid method is more reliable in handling diverse nonlinear behaviors. Therefore, the appropriate method selection should consider both the nature of the function and the need for speed or stability in the computation.

Laguerre-like methods for the simultaneous approximation of polynomial multiple zeros

Two new methods of the fourth order for the simultaneous determination of multiple zeros of a polynomial are proposed. The presented methods are based on the fixed point relation of Laguerre's type and realized in ordinary complex arithmetic as well as circular complex interval arithmetic. The derived iterative formulas are suitable for the construction of modified methods with improved convergence rate with negligible additional operations. Very fast convergence of the considered methods is illustrated by two numerical examples

A short survey on Kantorovich-like theorems for Newton's method

We survey influential quantitative results on the convergence of the Newton iterator towards simple roots of continuously differentiable maps defined over Banach spaces. We present a general statement of Kantorovich's theorem, with a concise proof from scratch, dedicated to wide audience. From it, we quickly recover known results, and gather historical notes together with pointers to recent articles

Attitude determination using vector observations: A fast optimal matrix algorithm

The attitude matrix minimizing Wahba's loss function is computed directly by a method that is competitive with the fastest known algorithm for finding this optimal estimate. The method also provides an estimate of the attitude error covariance matrix. Analysis of the special case of two vector observations identifies those cases for which the TRIAD or algebraic method minimizes Wahba's loss function

Formation and evolution of the protoplanetary disk

A disk formation model during collapse of the protosolar nebula, yielding a low-mass protoplanetary disk is presented. The following subject areas are covered: (1) circumstellar disks; (2) conditions for the formation of stars with disks; (3) early evolution of the protoplanetary disk; and (4) temperature conditions and the convection in the protoplanetary disk