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. 2019 May 10;6(Pt 4):586–602. doi: 10.1107/S2052252519005128

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© Ryan M. Trevorah et al. 2019

This is an open-access article distributed under the terms of the Creative Commons Attribution (CC-BY) Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original authors and source are cited.

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For the i-pr data set, the fractional correction from the denominator term in our test case is particularly small, even before Taylor expansion of the term. The fractional correction is as given in expression (10), as a function of energy and after inversion. Therefore, we expect the inversion to be relatively straightforward and to converge quickly and successfully, even though the exact solution of cubics and quartics can be challenging for mathematical software in the presence of noise.

Inline graphic — For the i-pr data set, the fractional correction from the denominator term in our test case is particularly small, even before Taylor expansion of the term. The fractional correction is as given in expression (10), as a function of energy and after inversion. Therefore, we expect the inversion to be relatively straightforward and to converge quickly and successfully, even though the exact solution of cubics and quartics can be challenging for mathematical software in the presence of noise.