In my experience as a researcher in computational numerics, the “standard library” is going to be defined by the in-house code that I use. That code is going to

In my experience as a researcher in computational numerics, the “standard library” is going to be defined by the in-house code that I use. That code is going to use other scientific libraries like for example PETSc, Atlas/blas/mkl, MPI in the background, but the typically researcher isn’t going to be exposed to that because their focus is on setting up the equation Ax = b and writing the algorithm to solve it for x.