Article ID Journal Published Year Pages File Type
5773826 Journal of Complexity 2017 28 Pages PDF
Abstract
Given a nonsingular n×n 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 O˜(nω⌈s⌉) 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 ω 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 O˜(nω) 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
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