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New approaches to error estimation to ill-posed problems with applications to inverse problems of heat conductivity
-
K.Y. Dorofeev
,
N.N. Nikolaeva
,
V.N. Titarenko
und
A.G. Yagola
Veröffentlicht/Copyright:
7. September 2013
Abstract
- In this paper several new approaches for error estimation of an approximate solution of linear ill-posed problems are offered in the presence of the additional a priori information about the exact solution. This information is used when the exact solution belongs to a compact set or is sourcewise represented. All considered problems are reduced to convex programming problems in finite dimensional Euclidean spaces. The method to cut convex polyhedrons is applied to solve these problems and to construct areas, which the exact solutions belong to. Several model inverse problems for the heat conduction equation are considered.
Published Online: 2013-09-07
Published in Print: 2002-05
© 2013 by Walter de Gruyter GmbH & Co.
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Artikel in diesem Heft
- Contents
- On inverse problem for a system of equations of elasticity theory
- Approximation of function with finite number of discontinuities by noised data
- The reconstruction of a vector field by finite difference methods
- New approaches to error estimation to ill-posed problems with applications to inverse problems of heat conductivity
- The linear sampling method in inverse obstacle scattering for impedance boundary conditions
- Recovering a vector field with the aid of controlled noise
- Beam-forming for nonlinear ultrasound inversion
Artikel in diesem Heft
- Contents
- On inverse problem for a system of equations of elasticity theory
- Approximation of function with finite number of discontinuities by noised data
- The reconstruction of a vector field by finite difference methods
- New approaches to error estimation to ill-posed problems with applications to inverse problems of heat conductivity
- The linear sampling method in inverse obstacle scattering for impedance boundary conditions
- Recovering a vector field with the aid of controlled noise
- Beam-forming for nonlinear ultrasound inversion
