A New Modified Levenberg–Marquardt Method for Systems of Nonlinear Equations
نویسندگان
چکیده
Taking a new choice of the LM parameter ? k = ? J T F ? with id="M2"> ? open="(" close="]" 0,2 , we give modified Levenberg–Marquardt method. Under error bound condition id="M3"> c dist close=")" w , S ? which is weaker than nonsingular Jacobian id="M4"> present that method has at least superlinear convergence when id="M5"> 0,1 and quadratic id="M6"> open="[" 1,2 respectively, indicates our performed for systems nonlinear equations. Also, numerical experiments indicate its efficiency on set
منابع مشابه
A MODIFIED STEFFENSEN'S METHOD WITH MEMORY FOR NONLINEAR EQUATIONS
In this note, we propose a modification of Steffensen's method with some free parameters. These parameters are then be used for further acceleration via the concept of with memorization. In this way, we derive a fast Steffensen-type method with memory for solving nonlinear equations. Numerical results are also given to support the underlying theory of the article.
متن کاملMultistage Modified Sinc Method for Solving Nonlinear Dynamical Systems
The sinc method is known as an ecient numerical method for solving ordinary or par-tial dierential equations but the system of dierential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical mod...
متن کاملA new optimal method of fourth-order convergence for solving nonlinear equations
In this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable Taylor and weight function approximation. The method is based on Weerakoon-Fernando method [S. Weerakoon, G.I. Fernando, A variant of Newton's method with third-order convergence, Appl. Math. Lett. 17 (2000) 87-93]. The method is optimal, as it needs three evaluations per iterate,...
متن کاملNew quasi-Newton method for solving systems of nonlinear equations
In this paper, we propose the new Broyden method for solving systems of nonlinear equations, which uses the first derivatives, but it is more efficient than the Newton method (measured by the computational time) for larger dense systems. The new method updates QR decompositions of nonsymmetric approximations of the Jacobian matrix, so it requires O(n) arithmetic operations per iteration in cont...
متن کاملA NEW MODIFIED HOMOTOPY PERTURBATION METHOD FOR SOLVING LINEAR SECOND-ORDER FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
In this paper, we tried to accelerate the rate of convergence in solving second-order Fredholm type Integro-differential equations using a new method which is based on Improved homotopy perturbation method (IHPM) and applying accelerating parameters. This method is very simple and the result is obtained very fast.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematics
سال: 2023
ISSN: ['2314-4785', '2314-4629']
DOI: https://doi.org/10.1155/2023/6043780