Implement Exciting-Mixing, Scalar and Diagonal Broyden approximations

[ChrisRackauckas]

https://docs.scipy.org/doc/scipy/reference/optimize.root-excitingmixing.html
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.diagbroyden.html#scipy.optimize.diagbroyden
https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linearmixing.html#scipy.optimize.linearmixing

[ChrisRackauckas]

@avik-pal is this completed as well?

[avik-pal]

No. Maybe let's transfer this to NonlinearSolve? We can handle all of them with branches in Broyden there

[avik-pal]

LinearMixing is just J = -1 / alpha, and J is never updated, I don't think there is any point of having that, for small problems our Broyden operates in nanoseconds via StaticArrays and for larger problems this won't work anyways

Even ExcitingMixing is a very crappy update rule, unless we have some compelling usecase for that, we should not clutter the implementation.