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.

arXiv comment26 pages