Parameter Identification for Nonlinear Ill-Posed Problems
نویسندگان
چکیده
منابع مشابه
Parameter Identification for Nonlinear Ill-posed Problems
Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s convergence in the light of Lyapunov theory. Furthermore, we consider 1-D elliptic type equation to testify that the homotopy regularization can ide...
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In this paper we consider nonlinear ill-posed problems with piecewise constant or strongly varying solutions. A class of nonlinear regularization methods is proposed, in which smooth approximations to the Heavyside function are used to reparameterize functions in the solution space by an auxiliary function of levelset type. The analysis of the resulting regularization methods is carried out in ...
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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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Straightforward solution of discrete ill-posed linear systems of equations or leastsquares problems with error-contaminated data does not, in general, give meaningful results, because propagated error destroys the computed solution. The problems have to be modified to reduce their sensitivity to the error in the data. The amount of modification is determined by a regularization parameter. It ca...
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ژورنال
عنوان ژورنال: Mathematical and Computational Applications
سال: 2010
ISSN: 2297-8747
DOI: 10.3390/mca15050790