  Hard X-ray spectra in solar flares provide knowledge of the electron spectrum
that results from acceleration and propagation in the solar atmosphere.
However, the inference of the electron spectra from solar X-ray spectra is an
ill-posed inverse problem. Here we develop and apply an enhanced regularization
algorithm for this process making use of physical constraints on the form of
the electron spectrum. The algorithm incorporates various features not
heretofore employed in the solar flare context: Generalized Singular Value
Decomposition (GSVD) to deal with different orders of constraints; rectangular
form of the cross-section matrix to extend the solution energy range;
regularization with various forms of the smoothing operator; and
"preconditioning" of the problem. We show by simulations that this technique
yields electron spectra with considerably more information and higher quality
than previous algorithms.
