In linear algebra, the same mathematical operation can be solved by different algorithms. This is of particular relevance in combination with techniques of automatic algorithm generation and tuning, in which dozens of algorithmic variants -- written in terms of BLAS (Basic Linear Algebra Subprograms) routines -- are produced. The algorithm of choice depends, obviously, on its performance. Performance of such algorithms is affected by a set of parameters, which characterize the features of the computing platform, the algorithm implementation, the size of the operands, and the
data storage format. Because of this complexity, predicting algorithmic performance is a challenging task, to the point that developers are often forced to rely on the extensive trial-and-error technique. We approach this problem from a different perspective. Instead of performing exhaustive tests, we introduce a technique for modeling performance that requires neither the execution of algorithms nor parts of them. This technique employs a bottom-up approach: we first model the performance of the BLAS kernels. Then, using these results we create models for higher-level algorithms, e.g.
the LU factorization, that are built on top of the BLAS kernels. As a result, by using the hierarchical and modular structure of linear algebra libraries, we develop a technique for hierarchical performance modeling that yields accurate predictions.