  We present the LU decomposition with panel rank revealing pivoting (LU_PRRP),
an LU factorization algorithm based on strong rank revealing QR panel
factorization. LU_PRRP is more stable than Gaussian elimination with partial
pivoting (GEPP). 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. 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. CALU_PRRP is more stable
than CALU, the communication avoiding version of GEPP. CALU_PRRP is also more
stable in practice and is resistant to pathological cases on which GEPP and
CALU fail.
