Create BisectionMethod.py

BisectionMethod.py

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+import math
+
+# Function to evaluate f(x) = x^3 - 2x - 5
+def calculate(x):
+    return (x * x * x) - (2 * x) - 5
+
+# Bisection method to find the root
+def bisection(a, b, tolerance, maxIter):
+    iteration = 0
+    c = 0
+
+    # Check if the initial guesses bracket the root
+    if calculate(a) * calculate(b) > 0:
+        print("Invalid values. f(a) and f(b) must have opposite signs.")
+        return None
+
+    # Iterative loop until the interval is smaller than tolerance or max iterations reached
+    while abs(b - a) > tolerance and iteration < maxIter:
+        c = (a + b) / 2
+
+        # Print the current iteration, mid-point, and its function value
+        print(f"Iteration {iteration + 1}: Root = {c}\tf(x) = {calculate(c)}")
+
+        # Check if the midpoint is the root
+        if calculate(c) == 0.0:
+            print(f"Exact root found: {c}")
+            return c
+
+        # Decide which subinterval to use in the next step
+        if calculate(a) * calculate(c) < 0:
+            b = c
+        else:
+            a = c
+
+        iteration += 1
+
+    # Final approximation after the loop ends
+    print(f"Final approximation after {iteration} iterations: Root = {c}\tf(x) = {calculate(c)}")
+    return c
+
+# Input values from the user
+a = float(input("Enter first guess value (a): "))
+b = float(input("Enter second guess value (b): "))
+tolerance = float(input("Enter the tolerance (e.g., 0.001): "))
+maxIter = int(input("Enter maximum number of iterations: "))
+
+# Call the bisection method
+bisection(a, b, tolerance, maxIter)