Approximate polynomial GCD (greatest common divisor) of polynomials with a priori errors on their coefficients, is one of interesting problems in Symbolic-Numeric Computations. In fact, there are many known algorithms: QRGCD, UVGCD, STLN based methods, Fastgcd and so on. The fundamental question of this paper is “which is the best?” from the practical point of view, and subsequently “is there any better way?” by any small extension, any effect by pivoting, and any combination of sub-routines along the algorithms. In this paper, we consider a framework that covers those algorithms and their sub-routines, and makes their sub-routines being interchangeable between the algorithms (i.e. disassembling the algorithms and reassembling their parts). By this framework along with/without small new extensions and a newly adapted refinement sub-routine, we have done many performance tests and found the current answer. In summary, 1) UVGCD is the best way to get smaller tolerance, 2) modified Fastgcd is better for GCD that has one or more clusters of zeros with large multiplicity, and 3) modified ExQRGCD is better for GCD that has no cluster of zeros.

系数具有先验误差的多项式的近似多项式GCD（最大公约数）是符号-数值计算中的一个有趣问题。实际上，有许多已知的算法：QRGCD，UVGCD，基于STLN的方法，Fastgcd等。本文的基本问题是“哪个最好？” 从实用的角度来看，随后“还有更好的方法吗？” 通过任何小的扩展，通过旋转实现的任何效果以及沿算法的子例程的任意组合。在本文中，我们考虑一个涵盖这些算法及其子例程的框架，并使它们的子例程在算法之间可互换（即，分解算法并重新组装其各个部分）。通过这个框架，加上/不包括小的新扩展和新改编的细化子例程，我们已经进行了许多性能测试并找到了当前答案。总而言之，1）UVGCD是获得较小公差的最佳方法，2）修改过的Fastgcd对于具有一个或多个零簇且多重性大的GCD更好，3）修改过的ExQRGCD对于没有零簇的GCD更好。