此篇論文在應用數值方法對實係數多項式做二次因式分解。我們所應用的基本方法是合併Bairstow的數值技巧與Gauss-Seidel疊代法以同時求得多項式的二次因式。這種方法的優點是可避免在計算機上的複數運算及作二次因子除法時的誤差累積。我們已將此數值演算法以數學軟體〝Mathematica〞編譯成程式。一些多項式經此程式所測試的結果呈現相當高的效率性與精確性。

In this paper, we present a numerical scheme to compute all quadratic factors of real polynomials simultaneously. This numerical technique is based on the Bairstow's method with the idea of Gauss-Seidel iteration. The advantage of this modified Bairstow's technique can avoid the complex arithmetic operation and the error accumulation of deflation. We also write the program in "Mathematica" to implement this scheme and have some computational results for the test polynomials.