Computing Popov and Hermite forms of polynomial matrices (1996)
| Venue: | In International Symposium on Symbolic and Algebmic Computation, Zutich, .%isse |
| Citations: | 19 - 10 self |
BibTeX
@INPROCEEDINGS{Villard96computingpopov,
author = {G. Villard},
title = {Computing Popov and Hermite forms of polynomial matrices},
booktitle = {In International Symposium on Symbolic and Algebmic Computation, Zutich, .%isse},
year = {1996},
pages = {250--258},
publisher = {ACM Press}
}
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Abstract
For a polynomial matrix P(z) of degree d in M~,~(K[z]) where K is a commutative field, a reduction to the Hermite normal form can be computed in O (ndM(n) + M(nd)) arithmetic operations if M(n) is the time required to multiply two n x n matrices over K. Further, a reduction can be computed using O(log~+ ’ (ml)) pamlel arithmetic steps and O(L(nd) ) processors if the same processor bound holds with time O (logX (rid)) for determining the lexicographically first maximal linearly independent subset of the set of the columns of an nd x nd matrix over K. These results are obtamed by applying in the matrix case, the techniques used in the scalar case of the gcd of polynomials.
