More matrix exponential methods

[jarlebring]

Wish-list / todo-list for more matrix exponential methods

• An implementation of A. H. Al-Mohy and N. J. Higham, A new scaling and squaring algorithm
  for the matrix exponential, SIAM J. Matrix Anal. Appl., 31(3), (2009) This is basically the same as Higham 2005, but with a more accurate backward error estimate which in practice leads to less multiplications. The method behind expm in recent versions of matlab.
• expmpoly: http://personales.upv.es/~jorsasma/software/expmpol.m described in Boosting the computation of the matrix exponential, Appl. Math. Comput., 2018 Requires only multiplications - no inverse. Main computation code can be generated with graph_exp_sid in GraphMatFun.jl.
• ExpMethodArbitraryPrecision. Arbitrary precision scaling-and-squaring: https://epubs.siam.org/doi/10.1137/18M1228876?mobileUi=0

[ChrisRackauckas]

Nice! Yeah, an arbitrary precision one would be very nice for the ecosystem. We've very much been missing it