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Hard X-ray spectra in solar flares provide knowledge of the electron spectrumthat results from acceleration and propagation in the solar atmosphere.However, the inference of the electron spectra from solar X-ray spectra is anill-posed inverse problem. Here we develop and apply an enhanced regularizationalgorithm for this process making use of physical constraints on the form ofthe electron spectrum. The algorithm incorporates various features notheretofore employed in the solar flare context: Generalized Singular ValueDecomposition (GSVD) to deal with different orders of constraints; rectangularform 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 techniqueyields electron spectra with considerably more information and higher qualitythan previous algorithms.Comment: 21 pages, 8 fugures, accepted to Solar Physic

Generalized Regularization Techniques with Constraints for the Analysis of Solar Bremsstrahlung X-ray Spectra