エイトケン加速
数列の収束する値を速く計算したい、という時に使うアルゴリズムである。
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from numba import jit
import numpy as np
import matplotlib.pyplot as plt
@jit
def f_aitken(s0,s1,s2):
return (s2 * s0 - s1 ** 2) / (s2 + s0 - 2 * s1)
@jit
def f_series(n):
series_list = [(-1) ** k / (2 * k + 1) for k in range(n+1)]
return series_list
@jit
def init_aitken(n):
x = f_series(n)
for i in range(n):
x[i + 1] = x[i] + x[i + 1]
return x
def main():
n = 10
series = init_aitken(n)
for i in range(2):
new_series = [0] * (n + 1)
for j in range(i + 1, n - i):
value = f_aitken(series[j - 1], series[j], series[j + 1])
new_series[j] = value
series = new_series
return series
x = main()
print(x)
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