  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.
