用近似法计算多项式元矩阵的行列式
Computing the determinant of a matrix with polynomial entries by approximation
摘要：
在科学计算和工程领域中，经常会遇到用一元和多元多项式计算矩阵行列式的问题。本文提出了一种用符号和数值混合计算方法计算多项式元矩阵行列式的有效算法。该算法依赖于误差控制的牛顿插值法求解范德蒙方程组。它也是基于一种新的方法来估计的程度的变量，和度同态方法降维。此外，该方法的并行化自然出现。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
