convergence domain

On convergence of function F4(1,2;2,2;z1,z2) expansion into a branched continued fraction

In the paper, the possibility of the Appell hypergeometric function ${F_4}(1,2; 2,2;{z_1},{z_2})$ approximation by a branched continued fraction of a special form is analysed.  The correspondence of the constructed branched continued fraction to the Appell hypergeometric function $F_4$ is proved.  The convergence of the obtained branched continued fraction in some polycircular domain of two-dimensional complex space is established, and numerical experiments are carried out.  The results of the calculations confirmed the efficiency of approximating the Appell hypergeomet

Local convergence analysis of the Gauss-Newton-Kurchatov method

We present a local convergence analysis of the Gauss-Newton-Kurchatov method  for solving nonlinear least squares problems with the decomposition of the operator.  The method uses the sum of the derivative of the differentiable part of the operator and the divided difference of the nondifferentiable part instead of computing  the full Jacobian.  A theorem, which establishes the conditions of convergence, radius, and the convergence order of the proposed method, is proved [1].  However, the radius of convergence is small in general limiting the choice of initial points.  Using tighter estima