diff --git a/linear regression/1.md b/linear regression/1.md
new file mode 100644
index 0000000..938f45d
--- /dev/null
+++ b/linear regression/1.md	
@@ -0,0 +1,18 @@
+# 1.py
+
+$$
+y = wx + b
+$$
+
+## 梯度下降算法
+
+$$
+b_gradient += -\frac{2}{N} \left(y - (w_current \cdot x + b_current)\right)
+$$
+
+
+
+$$
+w_gradient += -\frac{2}{N} \cdot x \cdot \left(y - (w_current \cdot x + b_current)\right)
+$$
+
diff --git a/linear regression/1.py b/linear regression/1.py
index dc455ef..a7402e6 100644
--- a/linear regression/1.py	
+++ b/linear regression/1.py	
@@ -19,8 +19,8 @@ def step_gradient(b_current, w_current, points, learningRate):
     for i in range(len(points)):
         x = points[i][0]
         y = points[i][1]
-        b_gradient += -(2 / N) * (y - (w_current * x + b_current) + b_current)
-        w_gradient += -(2 / N) * x * (y - (w_current * x + b_current + b_current))
+        b_gradient += -(2 / N) * (y - (w_current * x + b_current))
+        w_gradient += -(2 / N) * x * (y - (w_current * x + b_current))
     new_b = b_current - (learningRate * b_gradient)
     new_w = w_current - (learningRate * w_gradient)
     return [new_b, new_w]
diff --git a/linear regression/1_cuda.py b/linear regression/1_cuda.py
new file mode 100644
index 0000000..be818aa
--- /dev/null
+++ b/linear regression/1_cuda.py	
@@ -0,0 +1,67 @@
+import matplotlib.pyplot as plt
+import numpy as np
+import torch
+
+# 线性回归训练代码
+def compute_error_for_line_given_points(b, w, points):
+    totalError = 0
+    N = float(len(points))
+    for i in range(len(points)):
+        x = points[i][0]
+        y = points[i][1]
+        totalError += (y - (w * x + b)) ** 2
+    return totalError / N
+
+def step_gradient(b_current, w_current, points, learningRate):
+    b_gradient = torch.tensor(0.0, device=points.device)
+    w_gradient = torch.tensor(0.0, device=points.device)
+    N = float(len(points))
+    for i in range(len(points)):
+        x = points[i][0]
+        y = points[i][1]
+        b_gradient += -(2 / N) * (y - (w_current * x + b_current))
+        w_gradient += -(2 / N) * x * (y - (w_current * x + b_current))
+    new_b = b_current - (learningRate * b_gradient)
+    new_w = w_current - (learningRate * w_gradient)
+    return [new_b, new_w]
+
+def gradient_descent_runner(points, starting_b, starting_w, learningRate, num_iterations):
+    b = torch.tensor(starting_b, device=points.device)
+    w = torch.tensor(starting_w, device=points.device)
+    for i in range(num_iterations):
+        b, w = step_gradient(b, w, points, learningRate)
+    return [b, w]
+
+def run():
+    points_np = np.genfromtxt("data1.csv", delimiter=',').astype(np.float32)
+    points = torch.tensor(points_np, device='cuda')
+    learning_rate = 0.0001
+    initial_b = 0.0
+    initial_w = 0.0
+    num_iterations = 100000
+    [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
+    print("After gradient descent at b={0}, w={1}, error={2}".format(b.item(), w.item(),
+                                                                   compute_error_for_line_given_points(b, w, points)))
+    return b.item(), w.item()
+
+# 运行线性回归
+final_b, final_w = run()
+
+# 绘制图像
+points_np = np.genfromtxt("data1.csv", delimiter=',').astype(np.float32)
+x = points_np[:, 0]
+y = points_np[:, 1]
+
+x_range = np.linspace(min(x), max(x), 100)
+y_pred = final_w * x_range + final_b
+
+plt.figure(figsize=(8, 6))
+plt.scatter(x, y, color='blue', label='Original data')
+plt.plot(x_range, y_pred, color='red', label='Fitted line')
+plt.xlabel('X')
+plt.ylabel('Y')
+plt.title('Fitting a line to random data')
+plt.legend()
+plt.grid(True)
+plt.savefig('print1.png')
+plt.show()
diff --git a/linear regression/1x.py b/linear regression/1x.py
new file mode 100644
index 0000000..0b1b93a
--- /dev/null
+++ b/linear regression/1x.py	
@@ -0,0 +1,72 @@
+import matplotlib.pyplot as plt
+import numpy as np
+import torch
+
+
+# 线性回归训练代码
+def compute_error_for_line_given_points(b, w, points):
+    totalError = 0
+    N = float(len(points))
+    for i in range(len(points)):
+        x = points[i][0]
+        y = points[i][1]
+        totalError += (y - (w * x + b)) ** 2
+    return totalError / N
+
+
+def step_gradient(b_current, w_current, points, learningRate):
+    b_gradient = torch.tensor(0.0, device=points.device, dtype=torch.float32)
+    w_gradient = torch.tensor(0.0, device=points.device, dtype=torch.float32)
+    N = float(len(points))
+    for i in range(len(points)):
+        x = points[i][0]
+        y = points[i][1]
+        b_gradient += -(2 / N) * (y - (w_current * x + b_current))
+        w_gradient += -(2 / N) * x * (y - (w_current * x + b_current))
+    new_b = b_current - (learningRate * b_gradient)
+    new_w = w_current - (learningRate * w_gradient)
+    return [new_b, new_w]
+
+
+def gradient_descent_runner(points, starting_b, starting_w, learningRate, num_iterations):
+    b = torch.tensor(starting_b, device=points.device, dtype=torch.float32)
+    w = torch.tensor(starting_w, device=points.device, dtype=torch.float32)
+    for i in range(num_iterations):
+        b, w = step_gradient(b, w, points, learningRate)
+    return [b, w]
+
+
+def run():
+    points_np = np.genfromtxt("data1.csv", delimiter=',').astype(np.float32)
+    points = torch.tensor(points_np, device='mps')
+    learning_rate = 0.0001
+    initial_b = 0.0
+    initial_w = 0.0
+    num_iterations = 100000
+    [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
+    print("After gradient descent at b={0},w={1},error={2}".format(b.item(), w.item(),
+                                                                   compute_error_for_line_given_points(b, w, points)))
+    return b.item(), w.item()
+
+
+# 运行线性回归
+final_b, final_w = run()
+
+# 绘制图像
+points_np = np.genfromtxt("data1.csv", delimiter=',').astype(np.float32)
+x = points_np[:, 0]
+y = points_np[:, 1]
+
+x_range = np.linspace(min(x), max(x), 100)
+y_pred = final_w * x_range + final_b
+
+plt.figure(figsize=(8, 6))
+plt.scatter(x, y, color='blue', label='Original data')
+plt.plot(x_range, y_pred, color='red', label='Fitted line')
+plt.xlabel('X')
+plt.ylabel('Y')
+plt.title('Fitting a line to random data')
+plt.legend()
+plt.grid(True)
+plt.savefig('print1.png')
+plt.show()
diff --git a/linear regression/data1.csv b/linear regression/data1.csv
index 338b71d..508fd99 100644
--- a/linear regression/data1.csv	
+++ b/linear regression/data1.csv	
@@ -1,100 +1,100 @@
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diff --git a/linear regression/plt_print.py b/linear regression/plt_print.py
index 2e1d90c..245fe99 100644
--- a/linear regression/plt_print.py	
+++ b/linear regression/plt_print.py	
@@ -3,12 +3,13 @@ import matplotlib.pyplot as plt
 
 # 原始数据
 points = np.genfromtxt("data1.csv", delimiter=',')
+
 x = points[:, 0]
 y = points[:, 1]
 
 # 拟合直线
 x_range = np.linspace(min(x), max(x), 100)
-y_pred = 1.6455038785934448 * x_range + 1.827562689781189
+y_pred = 0.3880246877670288 * x_range + 1.7214288711547852
 
 # 绘图
 plt.figure(figsize=(8, 6))
diff --git a/linear regression/print1.png b/linear regression/print1.png
index a008b51..c2933e1 100644
Binary files a/linear regression/print1.png and b/linear regression/print1.png differ