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Figure 6
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 [(\mu / \rho) _{\rm pe,osc}^*] term. The fractional correction is as given in expression (10)[link], 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.

IUCrJ
Volume 6| Part 4| July 2019| Pages 586-602
ISSN: 2052-2525
https://doi.org/10.1107/S2052252519005128