Constrained Inversion for Finite-Difference Operators
, by Joe Dellinger
In SEP--50 I presented an inversion algorithm for finding accurate finite-difference operators. Each element of the finite-difference operator was a free
parameter in the inversion. The resulting objective function was unsuitable
for conjugate gradient techniques. The algorithm can be constrained easily by constructing the operators as weighted sums over a set of basis functions.
The inversion determines the weights of the basis functions, and not the
actual elements of the operator. This space of basis function weights is found
to be much more suitable for the use of conjugate gradient techniques than was
the descent space of the original problem.