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
Uniqueness of solution for the inverse problem of finding two minor coefficients in a semilinear time fractional telegraph equation
We find sufficient conditions of the uniqueness of a solution for the inverse problem of determining two continuous minor coefficients in a semilinear time fractional telegraph equation under two integral overdeterminati...
The interpolation functional polynomial: the analogue of the Taylor formula
The paper deals with a functional Newton type polynomial, which has two properties: the first one is that interpolation nodes are continual, that is, they depend on continuous parameters, and the second one is the invari...
Asymptotic properties of the impulse perturbation process under Levy approximation conditions with the point of equilibrium of the quality criterion
For the system of stochastic differential equations with Markov switchings and impulse disturbance in the conditions of Levy approximation in the conditions of a single point of equilibrium of the quality criterion, limi...
Distance between a maximum modulus point and zero set of an analytic function
Let f be an analytic function in the disk DR={z∈C:|z|≤R}, R∈(0,+∞]. We call a point w∈DR a maximum modulus point of f if |f(w)|=M(|w|,f), where M(r,f)=max{|f(z)|:|z|=r}. Denote by d(w,f) the distance between a maximum mo...
Lattices of coarse structures
We consider the lattice of coarse structures on a set X and study metrizable, locally finite and cellular coarse structures on X from the lattice point of view.