Polyhedral compiler technology is an advanced approach to optimizing the performance of programs through the analysis and transformation of loop nests, which are a common structure in iterative computations. It is named after the polyhedron, a geometric shape that represents the iteration space of nested loops.

The key idea behind polyhedral compilation is to model the program's loop nest as a mathematical polyhedron and use mathematical techniques to analyze and manipulate it. This allows for sophisticated optimizations that can exploit parallelism, improve data locality, and reduce loop overhead.