  Auxiliary matrix exponential method is used to derive simple and numerically
efficient general expressions for the following, historically rather cumbersome
and hard to compute, theoretical methods: (1) average Hamiltonian theory
following interaction representation transformations; (2)
Bloch-Redfield-Wangsness theory of nuclear and electron relaxation; (3)
gradient ascent pulse engineering version of quantum optimal control theory. In
the context of spin dynamics, the auxiliary matrix exponential method is more
efficient than methods based on matrix factorizations and also exhibits more
favourable complexity scaling with the dimension of the Hamiltonian matrix.
