关键词：LU分解；QR分解；数值实验；GEPP
摘 要：We present the LU decomposition with panel rank revealing pivoting (LU PRRP), an LU factorization algorithm based on strong rank revealing QR panel factorization. Our extensive numerical experiments show that the new factorization scheme is as numerically stable as GEPP in practice, but it is more resistant to pathological cases and easily solves the Wilkinson matrix and the Foster matrix. The LU PRRP factorization does onlyO(n2b) additional floating point operations compared to GEPP.We also present CALU PRRP, a communication avoiding version of LU PRRP that minimizes communication. CALU PRRP is based on tournament pivoting, with the selection of the pivots at each step of the tournament being performed via strong rank revealing QR factorization.