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  3. 1(2), 1999
  4. On the stable determination of some earth's radial density models

On the stable determination of some earth's radial density models

JGD.
1999;
Volume 1(2), 1999, Number 1(2), 1999
: 11-17
Authors:
  1. O. A. Abrikosov
1
Lviv Polytechnic National University

The regulanzation algorithm was developed on the basis of such Jit of the normal operator which is closed to a system of linear equations with scalar or unit matrix. The application of the famous theorem on the spectral expansion of normal matrixes Jed to introducing of the simplest matrix norm (connected with the traditional Euclidean norm) and allowed form special condition, which provides the determination of the regulanzation parameter. Proposed approach yieids the regulanzation parameter, which is responsible only for an accuracy of an initial operator and therefore, provides a stable inversion. Numerical testing of the algorithm was performed for the construction of piecewise density models of the Earth based on Roche's Gauss', and Legendre-Laplace laws.

regularization parameter
approximation of a normal operator
theorem on the spectral decomposition of normal matrices
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