1. A method of improving at least one of speed and efficiency when executing a level 3 dense linear algebra processing on a computer, said method comprising: automatically setting an optimal machine state on said computer for said processing by selecting an optimal matrix subroutine from among a plurality of matrix subroutines stored in a memory that could alternatively perform a level 3 matrix multiplication processing, wherein said computer includes an L1 cache, said method further comprising: determining a size of each of matrices involved in said matrix multiplication; and selecting one of said matrices to reside in an L1 cache, based on said determined size, wherein said selecting a matrix subroutine comprises determining which of said matrix subroutines is consistent with said matrix selected to reside in said L1 cache.