often necessary in order to eliminate spurious oscillatory features from the potentials. The operation of the SVD algorithm, with adjustable SVD limit, stabilises the inversion and can, where appropriate, reduce the effective dimensionality of the inversion basis.

Single-energy inversion {#firsttest}
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In Ref. [@prl] we presented a test of $S \rightarrow V$ for deuterons scattering from the light nucleus $^4$He in which there is very little absorption. Here we present a test for a much heavier nucleus, where there is substantial absorption, and demonstrate that a potential, very accurate almost to the nuclear centre, can be obtained by inversion. The test case studied was for a $^{58}$Ni target and deuterons at a laboratory energy of 56 MeV. The parameters found by Hatanaka [*et al*]{} [@hatanaka] fitting angular distributions and the analyzing powers $A_y$ and $A_{yy}$ were used. A notable feature of the potential was that the imaginary $T_{\rm R}$ term was quite large, but the real $T_{\rm R}$ term was very small (a common but unexplained feature of deuteron optical potentials.) The spin-orbit component was real. The potential was parity independent as expected for this combination of target, projectile and energy. The energy and other characteristics of the reaction are 