Localization algorithms for singularities of solutions to convolution equations of the first kind
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A. L. Ageev
Abstract
In this paper we construct and investigate localization algorithms for isolated singularities of a function which is a solution to a linear convolution equation of the first kind whose right-hand side is given with an error. We consider two types of singularities: δ-functions and discontinuities of the first kind. A problem for singularities localization is an ill-posed problem having perturbation. We use averaging methods defined by an averaging functional to obtain the singularities. We formulate conditions that the averaging functional must satisfy. For convolution equations, using the Fourier transform, we obtained upper estimates of precision of the singularities localization, separation threshold and other important characteristics of the supposed methods.
© de Gruyter 2008
Articles in the same Issue
- Localization algorithms for singularities of solutions to convolution equations of the first kind
- Unimprovable estimates of solutions for some classes of integral inequalities
- Relative computational efficiency of iteratively regularized methods
- Uniqueness of solution to an inverse problem for a semilinear system of partial differential equations
- Quasi-solution in inverse coefficient problems
- Inverse nodal problems for Sturm–Liouville operators on star-type graphs
- Fifth International Conference. Algorithmic Analysis of Unstable Problems (AAUP-2008)
Articles in the same Issue
- Localization algorithms for singularities of solutions to convolution equations of the first kind
- Unimprovable estimates of solutions for some classes of integral inequalities
- Relative computational efficiency of iteratively regularized methods
- Uniqueness of solution to an inverse problem for a semilinear system of partial differential equations
- Quasi-solution in inverse coefficient problems
- Inverse nodal problems for Sturm–Liouville operators on star-type graphs
- Fifth International Conference. Algorithmic Analysis of Unstable Problems (AAUP-2008)
