We present a deterministic algorithm, which, for any given 0< epsilon < 1 and
an nxn real or complex matrix A=(a_{ij}) such that | a_{ij}-1| < 0.19 for all
i, j computes the permanent of A within relative error epsilon in n^{O(ln n -ln
epsilon)} time. The method can be extended to computing hafnians and
multidimensional permanents.Comment: 12 pages, results extended to hafnians and multidimensional
permanents, minor improvement