
Bootstrapping interpolationThe bootstrapping algorithm for interpolation is based on Hermite interpolation, but does not reduce to it, since Hermite (on the two extremes of the integration interval and its derivatives) only gives 3rd order approximation.
When higher order is required, Hermite is first used to get the state at an intermediate point (but not the middle point for technical reasons) and then a new interpolation on the five data: states at both extremes, rates at both extremes, and the RATE on the intermediate point (but not its state, hence it not a threepoint Hermite interpolation) gives now one further order. This procedure is called bootstrapping and gives you order 4.
To increase to order 5, you need to repeat the procedure, starting now with the interpolation obtained in the previous step.
