In this work, numerical algebraic operations are performed by using several libraries whose algorithm are optimized to drain resources from hardware architecture. In particular, dot product of two vectors and the matrix-matrix product of two dense matrices are computed. In addition, the Cholesky decomposition on a real, symmetric, and positive definite matrix is performed through routines for band and sparse matrix storage. The involved CPU time is used as an indicator of the performance of the employed numerical tool. Results are compared to naive implementations of the same numerical algorithm, highlighting the speed-up due to the usage of optimized routines.