Zeros of Polynomial and an Estimation of its Accuracy

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Abstract

YAMASHITA S. and SATAKE S. show that the upper bound of the calculation errors of f(x)=ヨ?n_<k=0>a_kx^k is ヨ?n_<k=0>|a_kx^k|P^<-L> where L is the number of the digits in the mantissa based on P radix. We also show that near the zero of f(x) it is ヨ?n_<k=0>|a_kx^k|P^<-l>/2. Furthermore by using Newton-Raphson's iteration method we propose a method to estimate the accurate significant digits of the numerical result and give some numerical examples.

YAMASHITA, S. and SATAKE, S. show that the upper bound of the calculation errors of f(x)=ヨ\n_<k=0>a_kx^k is ヨ\n_<k=0>|a_kx^k|P^<-L>, where L is the number of the digits in the mantissa based on P radix. We also show that near the zero of f(x), it is ヨ\n_<k=0>|a_kx^k|P^<-l>/2. Furthermore by using Newton-Raphson's iteration method, we propose a method to estimate the accurate significant digits of the numerical result and give some numerical examples.

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