GPGCD，一种计算多个一元多项式近似GCD的迭代法
GPGCD, an Iterative Method for Calculating Approximate GCD, for Multiple Univariate Polynomials
摘要：
我们提出了我们的GPGCD方法，计算近似最大公因数（GCD）的一元多项式的迭代法，多个多项式输入的扩展。对于给定的一对多项式和一个次数，我们的算法找到一对多项式，它具有给定次数的GCD，并且其系数与原始输入中的系数相比被扰动，使得扰动尽可能小，同时具有GCD。在我们的GPGCD方法中，近似GCD问题转化为一个约束最小化问题，然后用所谓的变形牛顿法，这是一个推广的梯度投影法，通过迭代搜索的解决方案。在本文中，我们扩展我们的方法接受两个以上的多项式的实系数作为输入。
英文摘要：
We present an extension of our GPGCD method, an iterative method for calculating approximate greatest common divisor (GCD) of univariate polynomials, to multiple polynomial inputs. For a given pair of polynomials and a degree, our algorithm finds a pair of polynomials which has a GCD of the given degree and whose coefficients are perturbed from those in the original inputs, making the perturbations as small as possible, along with the GCD. In our GPGCD method, the problem of approximate GCD is transferred to a constrained minimization problem, then solved with the so-called modified Newton method, which is a generalization of the gradient-projection method, by searching the solution iteratively. In this paper, we extend our method to accept more than two polynomials with the real coefficients as an input.
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。
