We present a block LU factorization with panel rank revealing
pivoting (block LU_PRRP), an algorithm based on strong
rank revealing QR for the panel factorization.
Block LU_PRRP is more stable than Gaussian elimination with partial
pivoting (GEPP), with a theoretical upper bound of the growth factor
of $(1+ \tau b)^{(n/ b)-1}$, where $b$ is the size of the panel used
during the block factorization, $\tau$ is a parameter of the strong
rank revealing QR factorization, and $n$ is the number of columns of
the matrix. For example, if the size of the panel is $b = 64$, and
$\tau = 2$, then $(1+2b)^{(n/b)-1} = (1.079)^{n-64} \ll 2^{n-1}$, where
$2^{n-1}$ is the upper bound of the growth factor of 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 some pathological cases where GEPP fails. We note that the block LU_PRRP
factorization does only $O(n^2 b)$ additional floating point operations
compared to GEPP.