Bulletin of Computational Applied Mathematics (Bull CompAMa)
A constrained ill-posed linear problem with data in intervals arising in geodetic leveling
Henryk Gzyl, Silvia Mayoral
Ill-posed, linear inverse problems with convex constraints upon the solution and data in intervals do not admit easy solution with the traditional (penalized or not) least square based methodology. Using the geodetic leveling as a motivational example of this important class of inverse problems. Here we present an alternative approach to deal with such problems using the method of maximum entropy in the mean. This method allows us to deal with convex constraints, observational errors and data in intervals in an unified and efficient way.
Keywords: ill-posed linear inverse problems with convex constraints; problems with data in intervals; maximum entropy in the mean; geodetic leveling problem; networking problem.