BibTeX
@INCOLLECTION{
         Kubota2005CoM,
       author = "Koichi Kubota",
       title = "Computation of Matrix Permanent with Automatic Differentiation",
       editor = "H. M. B{\"u}cker and G. Corliss and P. Hovland and U. Naumann and B.
         Norris",
       booktitle = "Automatic Differentiation: {A}pplications, Theory, and Implementations",
       series = "Lecture Notes in Computational Science and Engineering",
       publisher = "Springer",
       year = "2005",
       abstract = "With a well-known formulation of matrix permanent by a multivariate polynomial,
         algorithms for the computation of the matrix permanent are considered in terms of automatic
         differentiation, where a succinct program with a C++ template for the higher order derivatives is
         described. A special set of commutative quadratic nilpotent elements is introduced, and it is shown
         that the permanent can be computed efficiently as a variation of implementation of higher order
         automatic differentiation. Given several ways for transforming the multivariate polynomial into
         univariate polynomials, six algorithms that compute the value of the permanent are described with
         their computational complexities. One of the complexities is O($n2^n$), the same as that of the most
         popular Ryser's algorithm.",
       crossref = "Bucker2005ADA",
       ad_area = "Matrix Permanent",
       ad_tools = "Padre2",
       pages = "67--76",
       doi = "10.1007/3-540-28438-9_6"
}