Fixed bug with incorrect LU decomposition (TheAlgorithms#2261)

* Fixed Bug TheAlgorithms#2257

* =

Co-authored-by: Svn-Sp <svn-sp@email>
Co-authored-by: Christian Clauss <[email protected]>

Author: 3 people

arithmetic_analysis/lu_decomposition.py

@@ -13,15 +13,15 @@ def LUDecompose(table):
     if rows != columns:
         return []
     for i in range(columns):
-        for j in range(i - 1):
+        for j in range(i):
             sum = 0
-            for k in range(j - 1):
+            for k in range(j):
                 sum += L[i][k] * U[k][j]
             L[i][j] = (table[i][j] - sum) / U[j][j]
         L[i][i] = 1
-        for j in range(i - 1, columns):
+        for j in range(i, columns):
             sum1 = 0
-            for k in range(i - 1):
+            for k in range(i):
                 sum1 += L[i][k] * U[k][j]
             U[i][j] = table[i][j] - sum1
     return L, U

arithmetic_analysis/newton_method.py

@@ -27,7 +27,7 @@ def newton(function: RealFunc, derivative: RealFunc, starting_int: int,) -> floa
     ...
     ZeroDivisionError: Could not find root
     """
-    prev_guess float(starting_int)
+    prev_guess = float(starting_int)
     while True:
         try:
             next_guess = prev_guess - function(prev_guess) / derivative(prev_guess)