Monotone interpolation: consider newer literature

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For example:

Huynh, H.T. (1993) ‘Accurate Monotone Cubic Interpolation’, SIAM Journal on Numerical Analysis, 30(1), pp. 57–100. Available at: https://doi.org/10.1137/0730004.

Wolberg, G. and Alfy, I. (2002) ‘An energy-minimization framework for monotonic cubic spline interpolation’, Journal of Computational and Applied Mathematics, 143(2), pp. 145–188. Available at: https://doi.org/10.1016/S0377-0427(01)00506-4.

Aràndiga, F. and Yáñez, D.F. (2019) ‘Third-order accurate monotone cubic Hermite interpolants’, Applied Mathematics Letters, 94, pp. 73–79. Available at: https://doi.org/10.1016/j.aml.2019.02.012.