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Abstract: In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. DeMol (2004) . This generalization is useful for solving many practical problems in which more than one constraint are involved. In this regard, we will conclude the findings of many papers (most of which are on image processing) from this generalization. It is hoped that the approach proposed in this paper will be a suitable reference for some applied works where multi-frames, multi-wavelets, or multi-constraints are present in linear inverse problems. [Copyright &y& Elsevier]

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]

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of regularized Gauss-Newton methods for solving nonlinear inverse problems for which an a posteriori stopping rule is proposed to terminate the iteration. Such methods have the frozen feature that they require only the computation of the Fréchet derivative at the initial approximation. Thus the computational work is considerably reduced. Under certain mild conditions, we give the convergence analysis and derive various estimates, including the order optimality, on these methods. [ABSTRACT FROM AUTHOR]