Added 'Gregory-Newton method'

Author: cfgnunes

README.md

@@ -52,6 +52,7 @@ python3 main.py
 
 - Lagrange method
 - Newton method
+- Gregory-Newton method
 - Neville method
 
 ### Algorithms for polynomials

interpolation.py

@@ -46,14 +46,42 @@ def newton(x, y, x_int):
         for i in range(m - 1, k - 1, -1):
             del_y[i] = (del_y[i] - del_y[i - 1]) / (x[i] - x[i - k])
 
-    # Evaluate the Newton polynomial
+    # Evaluate the polynomial by Horner's method
     y_int = del_y[-1]
     for i in range(m - 2, -1, -1):
         y_int = y_int * (x_int - x[i]) + del_y[i]
 
     return [y_int]
 
 
+def gregory_newton(x, y, x_int):
+    """Interpolates a value using the 'Gregory-Newton polynomial'.
+
+    Args:
+        x (numpy.ndarray): x values.
+        y (numpy.ndarray): y values.
+        x_int (float): value to interpolate.
+
+    Returns:
+        y_int (float): interpolated value.
+    """
+    m = x.size
+    del_y = y.copy()
+
+    # Calculate the finite differences
+    for k in range(1, m):
+        for i in range(m - 1, k - 1, -1):
+            del_y[i] = del_y[i] - del_y[i - 1]
+
+    # Evaluate the polynomial by Horner's method
+    u = (x_int - x[0]) / (x[1] - x[0])
+    y_int = del_y[-1]
+    for i in range(m - 2, -1, -1):
+        y_int = y_int * (u - i) / (i + 1) + del_y[i]
+
+    return [y_int]
+
+
 def neville(x, y, x_int):
     """Interpolates a value using the 'Neville polynomial'.
 

main.py

@@ -257,6 +257,24 @@ def example_interpolation_newton():
     print(f"y_int = {y_int:.5f}")
 
 
+@print_docstring
+def example_interpolation_gregory_newton():
+    """Run an example 'Interpolation: Gregory-Newton'."""
+    x = np.array([110, 120, 130])
+    y = np.array([2.0410, 2.0790, 2.1140])
+    x_int = 115
+
+    print("Inputs:")
+    print(f"x = {x}")
+    print(f"y = {y}")
+    print(f"x_int = {x_int}")
+
+    [y_int] = interpolation.gregory_newton(x, y, x_int)
+
+    print("Output:")
+    print(f"y_int = {y_int:.5f}")
+
+
 @print_docstring
 def example_interpolation_neville():
     """Run an example 'Interpolation: Neville'."""
@@ -703,6 +721,7 @@ def main():
     # Interpolation
     example_interpolation_lagrange()
     example_interpolation_newton()
+    example_interpolation_gregory_newton()
     example_interpolation_neville()
 
     # Algorithms for polynomials