This paper proposes an iterative method for solving an operator equation on a separable Hilbert space H equipped with a g-frame. We design an algorithm based on the conjugate gradient method and investigate the convergence and optimality of this algorithm. [ABSTRACT FROM AUTHOR]
The preconditioned iteratively regularized Gauss–Newton algorithm for the minimization of general nonlinear functionals was introduced by Smirnova, Renaut and Khan (Inverse Problems 23: 1547–1563, 2007). In this paper, we establish theoretical convergence results for an extended stabilized family of Generalized Preconditioned Iterative methods which includes ℳ-times iterated Tikhonov regularization with line search. Numerical schemes illustrating the theoretical results are also presented. [ABSTRACT FROM AUTHOR]
In this study, we apply optimal control approaches and adjoint equations to construct iterative processes for some problems of hydrodynamics. First, the iterative processes are proposed for an abstract problem given by the system of operator equations. Second, the general methodology is applied to the generalized Stokes equations perturbed by a skew-symmetric bounded operator and to the stationary linearized Navier–Stokes equations (the Oseen problem). The convergence rates of the iterative algorithms are studied. [ABSTRACT FROM AUTHOR]
We consider here the inverse problem, which consists in recovery of a nonlinear source in the equation of hyperbolic type with constant coefficients in main part of differential operator. The additional information for solution of the inverse problem is given in the form of final overdetermination. The iterative algorithm for recovery of the source is based on the theorem of existence and uniqueness of solution for the inverse problem that is proved in small. The convergence of the iterative method for solving the inverse problem is established. [ABSTRACT FROM AUTHOR]