In this work the architecture of an automatically tuned linear algebra library propose in previous works is extended in order to adapts itself to platforms where both the CPU load and the network traffic vary. During the installation process in a system, the linear algebra routines will be tuned automatically to the system conditions: hardware characteristics and basic libraries used in the linear algebra routines. At run-time the parameters that define the system characteristics are a justed to the actual load of the platform. The design methodology is analyse with a block LU factorisation. Variants for sequential and parallel versions of this routine on a logical rectangular mesh of processors are considered. The behavior of the algorithm is studied with message-passing, using MPI on a cluster of PCs. The experiments show that the configurable parameters of the linear algebra routines can be adjusted during the run-time process despite the variability of the environment.