On Some Multipoint Methods Arrising from Optimal in the Sense of Kung-Traub Algorithms for Numerical Solution of Nonlinear Equations
نویسندگان
چکیده
منابع مشابه
On some multipoint methods arising from optimal in the sense of Kung–Traub algorithms
In this paper we will examine self-accelerating in terms of convergence speed and the corresponding index of efficiency in the sense of Ostrowski–Traub of certain standard and most commonly used in practice multipoint iterative methods using several initial approximations for numerical solution of nonlinear equations due to optimal in the sense of the Kung–Traub algorithm of order 4, 8 and 16. ...
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بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
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A general class of three-point iterative methods for solving nonlinear equations is constructed. Its order of convergence reaches eight with only four function evaluations per iteration, which means that the proposed methods possess as high as possible computational efficiency in the sense of the Kung-Traub hypothesis (1974). Numerical examples are included to demonstrate a spectacular converge...
متن کاملOn the Kung-Traub Conjecture for Iterative Methods for Solving Quadratic Equations
Kung-Traub’s conjecture states that an optimal iterative method based on d function evaluations for finding a simple zero of a nonlinear function could achieve a maximum convergence order of 2d−1. During the last years, many attempts have been made to prove this conjecture or develop optimal methods which satisfy the conjecture. We understand from the conjecture that the maximum order reached b...
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ژورنال
عنوان ژورنال: BIOMATH
سال: 2013
ISSN: 1314-7218,1314-684X
DOI: 10.11145/j.biomath.2013.05.155