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The impact of this paper is twofold. First, we study convergence rates of the iteratively regularized Gauss-Newton (IRGN) algorithm with a linear penalty term under a generalized source assumption and show how the regularizing properties of new iterations depend on the solution smoothness. Secondly, we introduce an adaptive IRGN procedure, which is investigated under a relaxed smoothness condition. The introduction and analysis of a more general penalty term are of great importance since, apart from bringing stability to the numerical scheme designed for solving a large class of applied inverse problems, it allows us to incorporate various types of a priori information available on the model. Both a priori and a posteriori stopping rules are investigated. For the a priori stopping rule, optimal convergence rates are derived. A numerical example illustrating convergence rates is considered [ABSTRACT FROM AUTHOR]

This paper presents a method for identifying the general-order poles of a meromorphic function algebraically from its values on the unit circle, which has various applications in inverse source problems in potential analysis. First, we derive a system of Dth-degree equations for N distinct poles zn of order Dn, where n = 1, 2, . . . ,N and D = max1≤n≤N{Dn}. Then, we transform these equations into linear equations for the coefficients of the Nth-degree equation whose roots are zn so that the poles are obtained algebraically from data. The obtained poles can be used as an initial solution for iterative algorithms. A method for estimating the order Dn of each pole is also proposed and is numerically verified. [ABSTRACT FROM AUTHOR]