diff --git a/89-1.py b/89-1.py
index 84a3ccd..44a4ef1 100644
--- a/89-1.py
+++ b/89-1.py
@@ -43,6 +43,14 @@ def SovleRowMain(A,b):
 # 最小二乘法拟合
 def LeastSquares(list_x,list_y,n):
     m = len(list_x)
+    for i in range(2*n):
+        tl = [list_x[j]**(i+1) for j in range(m)]
+        print(f"x^{i+1} :",tl)
+        print("sum:", sum(tl))
+    for i in range(n+1):
+        tl = [list_y[j]*list_x[j]**i for j in range(m)]
+        print(f"y*x^{i}: ",tl)
+        print("sum:", sum(tl))
     x_n = []
     b = []
     for i in range(2*n+1):
@@ -71,13 +79,16 @@ def CalculateY(list_x, coeff):
         re.append(0)
         for j in range(len(coeff)):
             re[i] += coeff[j]*list_x[i]**j
+    print("y预测:", re)
     return re
 
 # 计算均方根误差
 def MeanSquareErr(list_y,list_y_approx):
     m = len(list_y)
     err = 0
+    print("y差值: ")
     for i in range(m):
+        print(f"y-y测={list_y[i] - list_y_approx[i]}, (y-y测)^2={(list_y[i] - list_y_approx[i])**2}")
         err += (list_y[i] - list_y_approx[i])**2
     return err**0.5
 
@@ -108,17 +119,19 @@ if __name__ == "__main__":
     coeff = LeastSquares(x,y,1)
     PrintEquation(coeff)
     y_approx = CalculateY(x, coeff)
-    print("均方根误差:")
-    print(MeanSquareErr(y,y_approx))
-    print("最大误差:")
-    print(MaxErr(y,y_approx))
+    # print()
+    print("均方根误差:",MeanSquareErr(y,y_approx))
+    # print()
+    print("最大误差:",MaxErr(y,y_approx))
+
+    print()
 
     print("二次拟合")
     coeff = LeastSquares(x,y,2)
     PrintEquation(coeff)
     y_approx = CalculateY(x, coeff)
-    print("均方根误差:")
-    print(MeanSquareErr(y,y_approx))
-    print("最大误差:")
-    print(MaxErr(y,y_approx))
+    # print()
+    print("均方根误差:",MeanSquareErr(y,y_approx))
+    # print()
+    print("最大误差:",MaxErr(y,y_approx))
     
\ No newline at end of file
diff --git a/按方法整理/拟合-最小二乘法.py b/按方法整理/拟合-最小二乘法.py
index 5d70403..e3dc779 100644
--- a/按方法整理/拟合-最小二乘法.py
+++ b/按方法整理/拟合-最小二乘法.py
@@ -48,6 +48,14 @@ def SovleRowMain(A,b):
 # 最小二乘法拟合
 def LeastSquares(list_x,list_y,n):
     m = len(list_x)
+    for i in range(2*n):
+        tl = [list_x[j]**(i+1) for j in range(m)]
+        print(f"x^{i+1} :",tl)
+        print("sum:", sum(tl))
+    for i in range(n+1):
+        tl = [list_y[j]*list_x[j]**i for j in range(m)]
+        print(f"y*x^{i}: ",tl)
+        print("sum:", sum(tl))
     x_n = []
     b = []
     for i in range(2*n+1):
@@ -76,13 +84,16 @@ def CalculateY(list_x, coeff):
         re.append(0)
         for j in range(len(coeff)):
             re[i] += coeff[j]*list_x[i]**j
+    print("y预测:", re)
     return re
 
 # 计算均方根误差
 def MeanSquareErr(list_y,list_y_approx):
     m = len(list_y)
     err = 0
+    print("y差值: ")
     for i in range(m):
+        print(f"y-y测={list_y[i] - list_y_approx[i]}, (y-y测)^2={(list_y[i] - list_y_approx[i])**2}")
         err += (list_y[i] - list_y_approx[i])**2
     return err**0.5
 
@@ -117,17 +128,16 @@ if __name__ == "__main__":
     coeff = LeastSquares(list_x,list_y,1)
     PrintEquation(coeff)
     y_approx = CalculateY(list_x, coeff)
-    print("均方根误差:")
-    print(MeanSquareErr(list_y,y_approx))
-    print("最大误差:")
-    print(MaxErr(list_y,y_approx))
+    print("均方根误差:",MeanSquareErr(list_y,y_approx))
+    print("最大误差:",MaxErr(list_y,y_approx))
 
+    print()
+    
     print("二次拟合")
     coeff = LeastSquares(list_x,list_y,2)
     PrintEquation(coeff)
     y_approx = CalculateY(list_x, coeff)
-    print("均方根误差:")
-    print(MeanSquareErr(list_y,y_approx))
-    print("最大误差:")
-    print(MaxErr(list_y,y_approx))
+    print("均方根误差:",MeanSquareErr(list_y,y_approx))
+    print("最大误差:",MaxErr(list_y,y_approx))
+
     
\ No newline at end of file
diff --git a/按方法整理/矩阵-列主元高斯消元法.py b/按方法整理/矩阵-列主元高斯消元法.py
index 80fc456..27bbf1f 100644
--- a/按方法整理/矩阵-列主元高斯消元法.py
+++ b/按方法整理/矩阵-列主元高斯消元法.py
@@ -22,6 +22,11 @@ def SovleRowMain(A,b):
         b[i], b[row_max_index] = b[row_max_index], b[i]
         p[i], p[row_max_index] = p[row_max_index], p[i]
 
+        print(f"第{i+1}次交换，交换行{i+1}和行{row_max_index+1}，A矩阵为：")
+        for row in A:
+            print(row)
+        print(f"b向量为：{b}\n")
+
         if abs(A[i][i]) < ks:
             print("A矩阵奇异，无法进行高斯消元")
             return None,None,None,None
@@ -31,6 +36,11 @@ def SovleRowMain(A,b):
             for k in range(i + 1, n):
                 A[j][k] -= m * A[i][k]
             b[j] -= m * b[i]
+            print(f"系数为{-1*m}用加号")
+        print("消元后的A矩阵：")
+        for row in A:
+            print(row)
+        print(f"消元后的b向量：{b}\n")
 
     if abs(A[n - 1][n - 1]) < ks:
         print("A矩阵奇异，无法进行高斯消元")
diff --git a/按方法整理/矩阵-平方根法.py b/按方法整理/矩阵-平方根法.py
index c0ce8ed..ef1c8ee 100644
--- a/按方法整理/矩阵-平方根法.py
+++ b/按方法整理/矩阵-平方根法.py
@@ -24,12 +24,25 @@ def SqrtSolve(A,b):
                 for k in range(j):
                     L[getIndexFromDownMatrix(i,j)] -= L[getIndexFromDownMatrix(i,k)]*L[getIndexFromDownMatrix(j,k)]
                 L[getIndexFromDownMatrix(i,j)] /= L[getIndexFromDownMatrix(j,j)]
-    print(L)
+
+    # 打印下三角矩阵
+    print("下三角矩阵 L:")
+    for i in range(n):
+        L_row = []
+        for j in range(n):
+            if j <= i:
+                L_row.append(L[getIndexFromDownMatrix(i,j)])
+            else:
+                L_row.append(0)
+        print(L_row)
+    # print(L)
     for i in range(n):
         for k in range(i):
             b[i] -= L[getIndexFromDownMatrix(i,k)]*b[k]
         b[i] /= L[getIndexFromDownMatrix(i,i)]
-
+    # 打印 b 向量
+    print("y 向量:")
+    print(b)
     for i in range(n-1,-1,-1):
         for k in range(i+1,n):
             b[i] -= L[getIndexFromDownMatrix(k,i)]*b[k]
@@ -45,5 +58,5 @@ if __name__ == "__main__":
 
     b = [10,5,4]    # b向量，常数项
 
-    print("x:")
-    print(SqrtSolve(A,b))
+    # print("x:")
+    print("x: \n",SqrtSolve(A,b))