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Mathematics Research Report MRR95-085
A Mollification Framework For Improperly Posed Problems
M. Hegland and R.S. Anderssen
Abstract:
Using classical semi-group results, a quite general theory is
constructed for the mollificaiton of operator equations, where the
operators are assumed to be translational invariant, and the choice of
mollifier is quite general and includes B-splines as well as the more
classical Gaussians. Among other things, specific conditions are derived
which establish how the discretization must be related to the extent of
the mollification in order to guarantee convergence and the boundedness
of the error amplification. In addition, explicit procedures are given
for the construction of finite difference formulas (stencils), and then
applied to the ordinary and half-differentiation of observational data.
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