2014/08/25 by Xiaolin Qin, Zhihong Sun, Zhi Sun +6
Computer Science · #15A15 #41A05 #65Y10 #68W30 #FOS: Computer and information sciences #Matrix Theory and Algorithms #Numerical Methods and Algorithms #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC #msc:15A15 #msc:41A05 #msc:65Y10 #msc:68W30
paper · pdf · doi:10.48550/arxiv.1408.5879
17 pages, 2 figures
openalex publication_date 2014/08/25 · arxiv created 2015/04/12 · arxiv updated 2015/04/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton's interpolation method with error control for solving Vandermonde systems. It is also based on a novel approach for estimating the degree of variables, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.