Further Results on Inversion of Aerosol Size Distribution Data: Higher-Order Sobolev Spaces and Constraints

The aerosol size distribution inversion algorithm of Crump and Seinfeld, based on the concept of regularization with generalized cross-validation, is extended to Sobolev spaces of order m. The use of the cross-validation function for choice of an appropriate value of m in a particular application is discussed. An inversion algorithm that constrains the size distribution to be nonnegative is introduced and shown to be of value for sharply peaked distributions.