Left-looking to right-looking and vice versa: An application of fractal symbolic analysis to linear algebra code restructuring

Abstract

We have recently developed a new program analysis strategy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis. In this paper, we show how fractal symbolic analysis can be used to convert between left-looking and right-looking versions of three kernels of central importance in computational science: Cholesky factorization, LU factorization with pivoting, and triangular solve.