The process of finding the solution of a linear system of equations is often the core of many scientific applications. Usually, this process relies upon the LU factorization, which is also the most compute-intensive part of it. Although current implementations of the LU fac-torization may reach 70% of the peak performance, their accuracy and, even more, reproducibility cannot be guaranteed, mainly, due to the non-associativity of floating-point operations and dynamic thread scheduling. In this work, we address the problem of reproducibility of the LU factorization due to cancelations and rounding errors, resulting from floating-point arithmetic. Instead of developing a completely independent version of the LU factorization, we benefit from the hierarchical structure of linear algebra libraries and start from develop-ing/enhancing reproducible algorithmic variants for the kernel operations like the ones included in the BLAS library-that serve as building blocks in the LU factorization. In addition, we aim at ensuring the accuracy of these underlying BLAS routines.