Convergence analysis of the Gauss-Newton- Potra method for nonlinear least squares problems
Journal Title: Математичні Студії - Year 2018, Vol 50, Issue 2
Abstract
In this paper we study an iterative differential-difference method for solving nonlinear least squares problems with nondifferentiable residual function. We have proved theorems which establish the conditions of convergence, radius and the convergence order under Lipschitz and ω-conditions for the first-order derivatives of the differentiable part and for the first and second orders divided differences of the nondifferentiable part of the nonlinear function. The carried numerical experiments demonstrate the efficiency of the proposed method.
Authors and Affiliations
S. M. Shakno, H. P. Yarmola, Yu. V. Shunkin
Relative growth of Dirichlet series
Let F and G be entire functions given by Dirichlet series with exponents increasing to +∞. In the term of generalized order it is introduced a concept of their relative growth and its connection with the growth of F and...
An extremal problem for volume functionals
We consider the class of ring Q-homeomorphisms with respect to p-modulus in Rn with p>n, and obtain a lower bound for the volume of images of a ball under such mappings. In particular, the following theorem is proved in...
The analogue of Bernstein’s inverse theorem for the one class of the space of sequences (in Ukrainian)
We introduce the space of numerical sequences lp={x=(ξk)∞k=1:|x|=∑∞k=1|ξk|pk≤+∞} with a quasi-norm |⋅| for an every sequence p=(pk)∞k=1 of numbers pk from the interval (0,1] and we prove the analogue of the inverse of Be...
On the growth of Laplace-Stieltjes integrals
In the paper it is investigated the growth of characteristics of Laplace-Stieltjes integrals I(σ)=∫+∞0f(x)dF(x), where F is a nonnegative nondecreasing unbounded function continuous on the right on [0,+∞) and f is a nonn...
Automorphism groups of superextensions of groups
A family L of subsets of a set X is called {\em linked} if A∩B≠∅ for all A,B∈L. A linked family M is {\em maximal linked} if M coincides with each linked family L on X that contains M. The superextension λ(X) consists of...