In this paper, we consider the problem of formulating the subresultant polynomials for several univariate polynomials in Newton basis. It is required that the resulting subresultant polynomials be expressed in the same Newton basis as that used in the input polynomials. To solve the problem, we devise a particular matrix with the help of the companion matrix of a polynomial in Newton basis. Meanwhile, the concept of determinantal polynomial in power basis for formulating subresultant polynomials is extended to that in Newton basis. It is proved that the generalized determinantal polynomial of the specially designed matrix provides a new formula for the subresultant polynomial in Newton basis, which is equivalent to the subresultant polynomial in power basis. Furthermore, we show an application of the new formula in devising a basis-preserving method for computing the gcd of several Newton polynomials.

翻译：本文研究在牛顿基下为多个一元多项式构造子结式多项式的问题。要求所得子结式多项式必须与输入多项式采用相同的牛顿基表示。为解决该问题，我们借助牛顿基下多项式的友矩阵，设计了一个特殊矩阵。同时，将幂基中用于构造子结式的行列式多项式概念推广至牛顿基情形。证明表明，该特殊矩阵的广义行列式多项式给出了牛顿基下子结式多项式的新公式，该公式与幂基下的子结式多项式等价。此外，我们展示了这一新公式在构建保持基结构的牛顿多项式最大公因式计算方法中的应用。