Higher-order composition of a symmetric splitting
= Higher-order composition of a symmetric splitting
If $S_h$ is a symmetric second-order splitting, then $S_{\gamma h}S_{\delta h}S_{\gamma h}$ is fourth order for $\gamma=(2-2^{1/3})^{-1}$ and $\delta=-2^{1/3}(2-2^{1/3})^{-1}$. The identities $2\gamma+\delta=1$ and $2\gamma^3+\delta^3=0$ preserve the total step and cancel the leading odd defect.