EXPLICIT ANALYTICAL REPRESENTATIONS OF SOLUTIONS OF THE LINEAR INVERSE PROBLEMS OF GRAVIMETRY AND MAGNETOMETRY IN THE CASE IN WHICH THE GIVEN DATA ARE CONTINUOUS

Abstract

The inverse problems of gravimetry and magnetometry have been examined in earlier papers for the case in which we have approximate measured values of some finite set of bounded linear functionals defined on the sources of the field. In these papers, we constructed explicit (resolvent) representations of the solutions of linear problems formulated in this manner. The solution procedure entailed repeated solution of systems of linear algebraic equations of order N, where N is the number of approximate measured values of linear functionals that are available. Obviously, if N is large (N ≥ 1000), then such algorithms become too time-consuming. But in some situations that are of practical importance, we can use the procedure of taking the limit to construct representations of solutions of the inverse linear problems that lead to much more economical algorithms.