【數值計算方法】線性方程組的迭代解法-數值實驗

from formu_lib import *
import numpy as np

A=np.array([[-55,-5,12],        
            [21,36,-13],
            [24,7,47]])
b=np.array([41,52,12])

w=lambda t:0.1*t

xs,ys,ts=[],[],[]
for i in range(1,20):
    _,err=SORIter(A,b,w(i))
    xs.append(list(range(len(err+1))))
    ys.append(err)
    ts.append(f"SOR iter error with w={w(i)}")
    print(f"i={i}")

• w=0.1~0.5

• w=0.6~1.0

• w=1.1~1.5

• w=1.6~1.9

結論:w 接近1.8時,演算法就不收斂了,迭代次數越多,誤差越大.