Are linear algorithms always good for linear problems?
The question is, if there are linear optimal error algorithms for all linear problems. The answer is no, which is shown in this paper with a general construction, for which every linear algorithm has infinite error, but there is a mildly nonlinear algorithm with finite error, which can be made arbitrarily small if appropriate information is used. As an example the inversion of Laplace transform over a finite interval is considered, a problem arising in remote sensing.
scientific article; zbMATH DE number 3974185