  In the canonical ramp compression experiment, a smoothly-increasing load is
applied to the surface of the sample, and the particle velocity history is
measured at two or more different distances into the sample, at interfaces
where the surface of the sample can be probed. The velocity histories are used
to deduce a stress-density relation, usually using iterative Lagrangian
analysis to account for the perturbing effect of the impedance mismatch at the
interface. In that technique, a stress- density relation is assumed in order to
correct for the perturbation, and is adjusted until it becomes consistent with
the deduced stress-density relation. This process is subject to the usual
difficulties of nonlinear optimization, such as the existence of local minima
(sensitivity to the initial guess), possible failure to converge, and
relatively large computational effort. We show that, by considering the
interaction of successive characteristics reaching the interfaces, the
stress-density relation can be deduced directly by recursion rather than
iteration. This calculation is orders of magnitude faster than iterative
analysis, and does not require an initial guess. Direct recursion may be less
suitable for very noisy data, but it was robust when applied to trial data. The
stress-density relation deduced was identical to the result from iterative
Lagrangian analysis.
