论文标题
具有多个单变量多项式的Bézout矩阵的GPGCD算法
The GPGCD Algorithm with the Bézout Matrix for Multiple Univariate Polynomials
论文作者
论文摘要
我们提出了对GPGCD算法的修改，该算法已在我们先前的研究中提出，以计算2个具有实际系数和给定程度的超过2个单变量多项式的最大共同分裂（GCD）。在将近似GCD问题转移到受约束的最小化问题时，与使用Sylvester subsultant矩阵的原始GPGCD算法不同，该算法使用Bézout矩阵。实验表明，对于多个多项式，所提出的算法比原始GPGCD算法更有效，在大多数情况下保持几乎相同的精度。
We propose a modification of the GPGCD algorithm, which has been presented in our previous research, for calculating approximate greatest common divisor (GCD) of more than 2 univariate polynomials with real coefficients and a given degree. In transferring the approximate GCD problem to a constrained minimization problem, different from the original GPGCD algorithm for multiple polynomials which uses the Sylvester subresultant matrix, the proposed algorithm uses the Bézout matrix. Experiments show that the proposed algorithm is more efficient than the original GPGCD algorithm for multiple polynomials with maintaining almost the same accuracy for most of the cases.
