Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4608566 | Journal of Complexity | 2015 | 12 Pages |
Abstract
Improved cost estimates are given for the problem of computing the inverse of an nÃn matrix of univariate polynomials over a field. A deterministic algorithm is demonstrated that has worst case complexity (n3s)1+o(1) field operations, where sâ¥1 is an upper bound for the average column degree of the input matrix. Here, the “+o(1)” in the exponent indicates a missing factor c1(logns)c2 for positive real constants c1 and c2. As an application we show how to compute the largest invariant factor of the input matrix in (nÏs)1+o(1) field operations, where Ï is the exponent of matrix multiplication.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Wei Zhou, George Labahn, Arne Storjohann,