Computing the Determinant of a Matrix with Polynomial Entries by Approximation |
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Authors: | Xiaolin Qin Zhi Sun Tuo Leng Yong Feng |
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Institution: | 1.Department of Mathematics,Sichuan University,Chengdu,China;2.Chengdu Institute of Computer Applications,Chinese Academy of Sciences,Chengdu,China;3.School of Computer Engineering and Science,Shanghai University,Shanghai,China |
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Abstract: | Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute 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. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally. |
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