Iterative processes of gradient type with applications to gravimetry and magnetometry inverse problems
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Vladimir Vasin
und
Georgy Skorik
Abstract
The iterative processes of gradient type for nonlinear equations with differentiable operator satisfying a local condition in the neighborhood of solution are investigated. The theorems on weak and strong convergence of iterations constructed by these methods and their modified analogs are established.
The inverse gravimetry problem is considered as the application of the developed methods: retrieval of the interface between the media with different constant densities. For stable solution of the nonlinear inverse magnetometry problem the additional regularization by the Tikhonov method is used and for approximation of the regularized solution one variant of the conjugate gradient method is applied. The numerical results for model and real gravitational and magnetic data are considered.
© de Gruyter 2011
Artikel in diesem Heft
- Inverse and ill-posed problems (Conference in Novosibirsk)
- Iterative processes of gradient type with applications to gravimetry and magnetometry inverse problems
- Some mathematical problems of acoustic probing
- Algorithm of finding a body projection within an absorbing and scattering medium
- Determination of physical and geometrical characteristics of layered inhomogeneous elastic medium
- On some classes of inverse problems for parabolic equations
- The optimum of the M. M. Lavrent'ev method
- Parameter identification methods of hydraulic models for the study of current water in open channels
Artikel in diesem Heft
- Inverse and ill-posed problems (Conference in Novosibirsk)
- Iterative processes of gradient type with applications to gravimetry and magnetometry inverse problems
- Some mathematical problems of acoustic probing
- Algorithm of finding a body projection within an absorbing and scattering medium
- Determination of physical and geometrical characteristics of layered inhomogeneous elastic medium
- On some classes of inverse problems for parabolic equations
- The optimum of the M. M. Lavrent'ev method
- Parameter identification methods of hydraulic models for the study of current water in open channels
