Про узагальнення теореми Ньютона–Канторовича для нелінійних операторних рівнянь, On the generalization of the Newton–Kantorovich theorem for nonlinear operator equations

<jats:p>UDC 517.98, 519.61 We construct a modification of the classical Newton-Kantorovich method for nonlinear operator equations whose linearization gives equations that are, as a rule, solvable. For finding the solution of a nonlinear operator equation, we propose to use an iterative scheme with quadratic convergence. In particular, we establish solvability conditions and construct an iterative procedure aimed at finding the solution of the generalized Riccati equation.</jats:p>