expm of Sastre, Ibanez, Defez

[jarlebring]

The manuscript "Boosting the computation of the matrix exponential"

https://doi.org/10.1016/j.amc.2018.08.017

needs to be added to the code generators, e.g. as gen_sid_exp.

It's a polynomial based procedure related to what is in bbc_exp.jl

• Should have similarities with bbc_exp.jl: gen_bbc_basic_exp
• Use calls to gen_general_poly_recursion

Moved from @mfasi's comment https://github.com/jarlebring/GraphMatFun.jl/issues/1#issuecomment-799764465

[jarlebring]

The SID method is much better than I thought. The general recursion has degree 16 with 4 multiplications, they manage to construct a polynomial that matches the Taylor polynomial for the exponential up to degree 15, compare to 12 with BBC and 9 with PS. Very close to optimal.

Note that they have a polynomial of degree 16, but only match the 16 first coefficient, not the 17th.

[jarlebring]

All the graphs presented in the paper are now in gen_sid_exp, but not the case determination. I think case determination is not the focus of the package so I will close this.