Preconditioning of Rectangular Polynomial Matrices for Eecient Hermite Normal Form Computation
نویسندگان
چکیده
We present a Las Vegas probabalistic algorithm for reducing the computation of Hermite normal forms of rectangular polynomial matrices. In particular, the problem of computing the Hermite normal form of a rectangular m n matrix (with m > n) reduces to that of computing the Hermite normal form of a matrix of size (n + 1) n having entries of similar coeecient size and degree. The main cost of the reduction is the same as the cost of fraction-free Gaussian elimination of an m n polynomial matrix. As an application , the reduction allows for the eecient computation of one-sided GCD's of two matrix polynomials along with the solution of the matrix diophantine equation associated to such a GCD.
منابع مشابه
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