THE USE OF LINEAR-PROGRAMMING IN THE CONSTRUCTION OF EXTREMAL SOLUTIONS TO LINEAR INVERSE PROBLEMS

While a finite collection of data does not specify a unique solution t o a linear inverse problem, it can allow bounds to be placed on certai n nonlinear solution functionals. Using the Dirichlet problem for the unit disc as an example, this note demonstrates the use of linear prog ramming in constructing extremal solutions associated with a variety o f such bounds.