The Accuracy of Multiple or Clustered Zeros Using Numerical Integration Error Method

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  • 数値積分誤差法による重根、近接根の計算精度
  • スウチ セキブン ゴサホウ ニ ヨル ジュウ コン キンセツ コン ノ ケイサン セイド

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The polynomial root-finding algorithm that uses the errors of numerical integration of the logarithmic derivative was announced. In this algorithm, a new approximate expression of zeros was proposed. We call the method NIEM (Numerical Integration Error Method). In general, the accuracy of the multiple zero is worse than that of the simple one. The reason for this deterioration of accuracy is that the polynomial and its differentiation is estimated in a neighborhood of the multiple zero. NIEM can avoid this deterioration by evaluating them away from the multiple zero. In this paper we propose an approach for multiple or clustered zeros using NIEM.

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