منابع مشابه
Solution of Ill-Posed Volterra Equations via Variable-Smoothing Tikhonov Regularization
We consider a “local” Tikhonov regularization method for ill-posed Volterra problems. In addition to leading to efficient numerical schemes for inverse problems of this type, a feature of the method is that one may impose varying amounts of local smoothness on the solution, i.e., more regularization may be applied in some regions of the solution’s domain, and less in others. Here we present pro...
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We develop a theoretical context in which to study the future-sequential regularization method developed by J. V. Beck for the Inverse Heat Conduction Problem. In the process, we generalize Beck’s ideas and view that method as one in a large class of regularization methods in which the solution of an ill-posed first-kind Volterra equation is seen to be the limit of a sequence of solutions of we...
متن کاملApproximation of Ill-posed Boussinesq Equations
In this paper we study finite dimensional approximations to Boussinesq type equations. Our methods are based on infinite dimensional center manifold theory. The main advantage of our approach is that we can handle both well-posed and ill-posed versions of the Boussinesq equation. We show that for suitable initial conditions, our approximations describe the dynamics accurately for long enough ti...
متن کاملTime-dependent Perturbations of Abstract Volterra Equations
AMS Mathematics Subject Classification (2000): 47D06, 47D60, 47D62, 47D99
متن کاملIll-Posed and Linear Inverse Problems
In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.
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ژورنال
عنوان ژورنال: Publications de l'Institut Mathematique
سال: 2013
ISSN: 0350-1302,1820-7405
DOI: 10.2298/pim1307049k