近似积和式
Approximating permanents and hafnians
摘要：
证明了n × n实矩阵A的积和式的对数和2n × 2n实对称矩阵A的积和式的对数在加法误差1 > n> 0的范围内可以用A的元中的一个0次多项式p（ln n - ln n）来逼近，只要A的元a_ij满足delta < a_ij < 1 for an arbitrarily small delta >0，预先确定.此外，多项式p可以在n^{O（ln n - ln n）}时间内计算。我们还改进了复矩阵和复张量A的多维积和式的逼近ln per A、ln haf A和近似的界。
英文摘要：
We prove that the logarithm of the permanent of an nxn real matrix A and the logarithm of the hafnian of a 2nx2n real symmetric matrix A can be approximated within an additive error 1 > epsilon > 0 by a polynomial p in the entries of A of degree O(ln n - ln epsilon) provided the entries a_ij of A satisfy delta < a_ij < 1 for an arbitrarily small delta > 0, fixed in advance. Moreover, the polynomial p can be computed in n^{O(ln n - ln epsilon)} time. We also improve bounds for approximating ln per A, ln haf A and logarithms of multi-dimensional permanents for complex matrices and tensors A.
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