Open AccessNon‐negative solutions and positive resolving kernels with negative solution averages in linear inverse theory
Author(s) -
Huestis Stephen P.
Publication year - 1993
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1993.tb01210.x
Subject(s) - mathematics , kernel (algebra) , inverse , inverse theory , inverse problem , duality (order theory) , mathematical analysis , pure mathematics , physics , geometry , deformation (meteorology) , meteorology
SUMMARY Using the duality theorem of linear programming, it is shown that, for a linear inverse problem, the non‐existence of a non‐negative solution is equivalent to the existence of a positive‐resolving kernel associated with a negative solution average. If no such resolving kernel can be found, we are then guaranteed the existence of a non‐negative solution.