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Figure 4
Examples of solutions of the cubic X-ray approximation [equation (57)[link]] at various values of [\delta] for a representative set of values for q1 (23.0929 m) and q2 (8.6912 m). The solutions of the cubic approximation are labelled y(x). The solutions `x(y)' were calculated by solving equation (18)[link] as a quadratic equation in x2 with y-dependent coefficients [see equation (45)[link]]. The top row demonstrates three cases in which [\delta \,\gt\, 0] and the bottom row demonstrates three cases in which [\delta \,\lt\, 0]. In each row, [\delta \to 0] from left to right. Note the loss of numerical precision in the solutions of the exact formula as [|\delta|] decreases, even while the cubic approximation remains numerically stable.

Journal logoJOURNAL OF
SYNCHROTRON
RADIATION
ISSN: 1600-5775
Volume 24| Part 6| November 2017| Pages 1120-1136
https://doi.org/10.1107/S1600577517011808
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