Name
Title | ||
|---|---|---|
Computing Mu-Bases Of Univariate Polynomial Matrices Using Polynomial Matrix Factorization |
Abstract | ||
|---|---|---|
This paper extends the notion of mu-bases to arbitrary univariate polynomial matrices and present an efficient algorithm to compute a mu-basis for a univariate polynomial matrix based on polynomial matrix factorization. Particularly, when applied to polynomial vectors, the algorithm computes a mu-basis of a rational space curve in arbitrary dimension. The authors perform theoretical complexity analysis in this situation and show that the computational complexity of the algorithm is O(dn(4)+d(2)n(3)), where n is the dimension of the polynomial vector and d is the maximum degree of the polynomials in the vector. In general, the algorithm is n times faster than Song and Goldman's method, and is more efficient than Hoon Hong's method when d is relatively large with respect to n. Especially, for computing mu-bases of planar rational curves, the algorithm is among the two fastest algorithms. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1007/s11424-020-9314-6 | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY |
Keywords | DocType | Volume |
Computational complexity, matrix factorization, mu-bases | Journal | 34 |
Issue | ISSN | Citations |
3 | 1009-6124 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bingru Huang | 1 | 0 | 0.34 |
| Falai Chen | 2 | 403 | 32.47 |