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, and 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 to investigate these areas.