Enabling Pivoting in the Formal Derivation of LU factorization

Abstract

The FLAME methodology for deriving linear algebra algorithms from specification, first introduced around 2000, has been successfully applied to a broad cross section of operations. An open question has been whether it can yield algorithms for the best-known operation in linear algebra, LU factorization with partial pivoting (Gaussian elimination with row swapping). This paper shows that it can and provides general techniques for pivoted factorizations.