Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773826 | Journal of Complexity | 2017 | 28 Pages |
Abstract
Given a nonsingular nÃn matrix of univariate polynomials over a field K, we give fast and deterministic algorithms to compute its determinant and its Hermite normal form. Our algorithms use OË(nÏâsâ) operations in K, where s is bounded from above by both the average of the degrees of the rows and that of the columns of the matrix and Ï is the exponent of matrix multiplication. The soft-O notation indicates that logarithmic factors in the big-O are omitted while the ceiling function indicates that the cost is OË(nÏ) when s=o(1). Our algorithms are based on a fast and deterministic triangularization method for computing the diagonal entries of the Hermite form of a nonsingular matrix.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
George Labahn, Vincent Neiger, Wei Zhou,