This paper tackles the problem of constructing Bezout matrices for Newton polynomials in a basis-preserving approach that operates directly with the given Newton basis, thus avoiding the need for transformation from Newton basis to monomial basis. This approach significantly reduces the computational cost and also mitigates numerical instability caused by basis transformation. For this purpose, we investigate the internal structure of Bezout matrices in Newton basis and design a basis-preserving algorithm that generates the Bezout matrix in the specified basis used to formulate the input polynomials. Furthermore, we show an application of the proposed algorithm on constructing confederate resultant matrices for Newton polynomials. Experimental results demonstrate that the proposed methods perform superior to the basis-transformation-based ones.

翻译：本文针对牛顿多项式Bezout矩阵的构造问题，提出了一种基保持方法。该方法直接利用给定牛顿基进行运算，避免了从牛顿基到单项基的转换需求。这种处理方式显著降低了计算开销，同时缓解了基变换引发的数值不稳定性。为此，我们深入研究了牛顿基下Bezout矩阵的内部结构，设计了一种基保持算法，该算法能够基于输入多项式所采用的特定基直接生成Bezout矩阵。此外，我们还展示了该算法在构建牛顿多项式联合结式矩阵中的应用。实验结果表明，所提方法在性能上优于基于基变换的传统方法。