That of course only covers the range of paths that are generated by the interpolation algorithm, with $k$ intermediate points.

So it gives an upper bound on the least action.

The next step they describe is run a loop in which $k$ is increased, and observe how these upper bounds decrease.

In the example they describe, it clearly converges to the value for least action which is obtained by analysis.

So it gives an upper bound on the least action.

The next step they describe is run a loop in which $k$ is increased, and observe how these upper bounds decrease.

In the example they describe, it clearly converges to the value for least action which is obtained by analysis.