A New Method to Compute Zeros of Polynomials Using the Errors of Numerical Integration

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  • 数値積分誤差を用いた新しい多項式の零点の解法
  • スウチ セキブン ゴサ オ モチイタ アタラシイ タコウシキ ノ レイテン ノ カイホウ

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The purpose of this paper is to introduce a new method to compute the zeros of polynomials. A lot of methods are available for the determination of the zeros of polynomials^[6]. The feature of our method is in using the errors of numerical integrals of the logarithmic derivative of the polynomial. Our method is explained in two algorithms. The fundamental algorithm finds the zero which is the nearest to the initial value as our theory indicates. We propose the applied algorithm as a practical one, which converges more quickly than dose the fundamental algorithm.

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