Positivity constraints in linear inverse problems. I - General theory. II - Applications

Details Positivity constraints in linear inverse problems. I - General theory. II - Applications Positivity constraints in linear inverse problems. I - General theory. II - Applications

Mar 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977geoj...48..415s&link_type=abstract

Geophysical Journal, vol. 48, no. 3, Mar. 1977, p. 415-441, 443-459. Centre National de la Recherche Scientifique

Computer Science

Numerical Analysis

24

Astrophysics, Boundary Value Problems, Constraints, Geophysics, Linear Equations, Range (Extremes), Applications Of Mathematics, Center Of Gravity, Curve Fitting, Error Analysis, Limits (Mathematics), Moments Of Inertia, Nonlinear Equations, Numerical Analysis, Planetary Gravitation

Scientific paper

This paper presentes a general method for solving linear inverse problems with either non-negative constraints or upper bounds or both. It is shown that for any finite problem approaching the exact one, there exists a finite set of extremal solutions and extremal directions such that any solution can be obtained from them by convex linear combinations. It is also shown how to substitute a finite problem for the exact problem in such a way that no information is lost. Several applications in geophysics are discussed, for example, the evolution of the set of solutions when a statistical distribution of errors is assumed. Some aspects of Parker's theory of ideal bodies (1974, 1975) are extended. Planar diagrams are studied showing two moments of a solution versus each other for all possible solutions. This technique can be extended to three-dimensional diagrams which can be used for gravity interpretation.

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