The challenge for the development of next generation software is the successful management of the complex computational environment while delivering to the scientist the full power of flexible compositions of the available algorithmic alternatives. Self-Adapting Numerical Software (SANS) systems are intended to meet this significant challenge. The process of arriving at an efficient numerical solution of problems in computational science involves numerous decisions by a numerical expert. Attempts to automate such decisions distinguish three levels:

• Algorithmic decision;
• Management of the parallel environment;
• Processor-specific tuning of kernels.

Additionally, at any of these levels we can decide to rearrange the user’s data. In this paper we look at a number of efforts at the University of Tennessee that are investigating these areas.