20250423

120-4.py

@@ -0,0 +1,25 @@
+def fx(x):
+    return 1/x
+
+
+def SplitTrapezoidal(a,b,err):
+    t1 = (b-a)*(fx(a)+fx(b))/2
+    k = 1
+    while True:
+        tmp = 0
+        for i in range(1, 2**(k-1)+1):
+            tmp += fx(a + (b-a)*(2*i-1)/(2**k))
+        t2 = t1/2+(b-a)*tmp/(2**k)
+        if abs(t2-t1) < err:
+            break
+        t1 = t2
+        k += 1
+    return t2,k
+
+
+if __name__ == "__main__":
+    a = 1
+    b = 3
+    err = 1e-2
+    result,k = SplitTrapezoidal(a, b, err)
+    print(f"Result: {result},k={k}")