Main constructive ideas underlying the development of numerical methods offinding stable approximate solutions to systems of linear algebraic equations with inaccurate right-hand sides in gravity and magnetic problems: I. Fundamental constructive ideas

The following three statements are substantiated. (1) The main numerical pr oblem of gravimetry and magnetometry is the search for stable approximate s olutions to systems of linear algebraic equations with inaccurate right-han d sides, (2) The existing (classical) regularization theory of systems of l inear algebraic equations is inadequate to real geophysical practice. (3) I t is vital to develop a regularization theory of systems of linear algebrai c equations that would fully match real geophysical practice. The main aspe cts of a new regularization theory of this type are presented.