2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56763A new continuous regularized Gauss-Newton-type method with simultaneous updates of the operator $(F^{\pr*}(x(t))F'(x(t))+\ep(t) I)^{-1}$ for solving nonlinear ill-posed equations in a Hilbert space is proposed. A convergence theorem is proved. An attractive and novel feature of the proposed method is the absence of the assumptions about the location of the spectrum of the operator $F'(x)$. The absence of such assumptions is made possible by a source-type condition.10ppMathematical Physics65J15, 58C15, 47H17text