aaa

按方法整理/非线性方程-抛物线法.py

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+import math
+
+
+#抛物线法解方程
+def MullerSolve(fx,x0,x1,x2,err1,err2,N):
+    count = 0
+    f0 = fx(x0)
+    f1 = fx(x1)
+    f2 = fx(x2)
+    q = (x2 - x1) / (x1 - x0)
+    p = 0
+    a = 0
+    b = 0
+    c = 0
+    while True:
+        p = (x2 - x0) / (x1 - x0)
+
+        a = q**2 * f0 - q*p*f1 + q*f2
+        b = q**2 *f0 - p**2 *f1 + (p + q)*f2
+        c = p*f2
+        h1 = 0
+        if b < 0:
+            h1 = -2 * c / (b - (b**2 - 4*a*c)**0.5)
+        else:
+            h1 = -2 * c / (b + (b**2 - 4*a*c)**0.5)
+        x3 = x2 + h1 * (x2 - x1)
+        f3 = fx(x3)
+
+        print(f"k={count}: x{count}={x0:.5}, f(x{count})={f0:.5}; x{count+1}={x1:.5}, f(x{count+1})={f1:.5}; x{count+2}={x2:.5}, f(x{count+2})={f2:.5}; x{count+3}={x3:.5}, f(x{count+3})={f3:.5}")
+        print(f"p={p:.5}, q={q:.5}, a={a:.5}, b={b:.5}, c={c:.5}, h={h1:.5}")
+
+        k = err1 + 1
+        if abs(f3) < 1:
+            k = abs(x3 - x2)
+        else:
+            k = abs(x3 - x2) / abs(f3)
+
+        if abs(f3) < err2 or k < err1:
+            return x3, 1
+        count += 1
+        if count > N:
+            return None, 0
+        x0 = x1
+        x1 = x2
+        x2 = x3
+        f0 = f1
+        f1 = f2
+        f2 = f3
+        q = h1
+
+
+if __name__ == "__main__":
+    err1 = 1e-5           # 精度要求    P152
+    err2 = 1e-5           # 精度要求    P152
+    N = 100               # 最大迭代次数
+    x0 = 0.3              # 初始值1
+    x1 = 0.5              # 初始值2
+    x2 = 0.4              # 初始值3
+    fx = lambda x: 8*x**4 - 8*x**2 + 1        #原函数
+
+    result, status = MullerSolve(fx, x0, x1, x2, err1, err2, N)
+    if status == 1:
+        print(f"fx收敛 解为: {result}")
+    else:
+        print("fx不收敛")