Third-order iterative methods without using any Fréchet derivative
نویسندگان
چکیده
منابع مشابه
THIRD-ORDER AND FOURTH-ORDER ITERATIVE METHODS FREE FROM SECOND DERIVATIVE FOR FINDING MULTIPLE ROOTS OF NONLINEAR EQUATIONS
In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.
متن کاملIterative Computation of the Fréchet Derivative Of
We derive iterative methods for computing the Fréchet derivative of the map which 4 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 5 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 6 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 7 identity that relates the ...
متن کاملthird-order and fourth-order iterative methods free from second derivative for finding multiple roots of nonlinear equations
in this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. each of them requires one evaluation of the function and two of its first derivative per iteration. several numerical examples are given to illustrate the performance of the presented methods.
متن کاملThird order iterative methods free from second derivative for nonlinear systems
In this paper, we present a class of new iterative methods, in which f ′(x) = 0 in some points is permitted. Analysis of convergence shows that the new methods are cubically convergent. Per iteration the new methods require one evaluation of the function and two of its first derivative, but no evaluations of its second derivative. Thus, the new methods have definite practical utility, which is ...
متن کاملIterative Computation of the Fréchet Derivative of the Polar Decomposition
We derive iterative methods for computing the Fréchet derivative of the map which sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices as well as rectangular matrices having more rows than columns. Our derivation relies on a novel identity that relates the Fréchet ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2003
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(03)00460-6