If you want to use a computational library on a high-performance computing center where you have no root access to install new software you can use header-only template libraries such as MTL4, Eigen3, GMM++ easily by including the library folder in the linking path. How about other libraries such as PetSc, Trilinos, Armadillo, Blaze, GSL,... that require compilation? Is there a way to use them on a machine where you have no root access if they are not preinstalled?
If you want to use Python libraries, you can even use the
pip package manager to install a package for your user account only with this invocation:
pip install --user <package>
Another possibility for Python is using
virtualenv, which allows you to set up isolated Python environments without the need for root access.