用5种方法求：y=t^3-2t+1的在区间[-3,5]之间的最小值。精度0.01的代码

要找函数 \( y = t^3 - 2t + 1 \) 在区间 \([-3, 5]\) 内的最小值，有多种数值计算方法可以实现，这里提供五种常见的搜索策略：

1. **二分法** (Bisection Method):

import math

def bisection(f, a, b, precision=0.01):
    if f(a)*f(b) >= 0:
        return None  # 函数在[a, b]无极值
    while b-a > precision:
        c = (a+b)/2
        if f(c) * f(a) < 0:
            b = c
        else:
            a = c
    return c, f(c)

# 定义函数
def func(t):
    return t**3 - 2*t + 1

min_value, min_t = bisection(func, -3, 5)

2. **牛顿迭代法** (Newton-Raphson Method):

def newton_raphson(f, df, x0, precision=0.01):
    while abs(f(x0)) > precision:
        x0 -= f(x0) / df(x0)
    return x0, f(x0)

def df(t):
    return 3*t**2 - 2

min_t, _ = newton_raphson(func, df, 2)  # 初始猜测点2

3. **梯度下降法** (Gradient Descent):

def gradient_descent(f, df, initial_guess, learning_rate, precision=0.01):
    x = initial_guess
    while abs(f(x)) > precision:
        x -= learning_rate * df(x)
    return x, f(x)

min_t, _ = gradient_descent(func, df, 2, 0.01)

4. **黄金分割搜索** (Golden Section Search):

from scipy.optimize import golden

def golden_search(f, a, b, precision=0.01):
    phi = (math.sqrt(5) + 1) / 2
    while (b - a) > precision:
        a_, b_ = a + (phi - 1) * (b - a), a + phi * (b - a)
        if f(a_) < f(b_):
            b = b_
        else:
            a = a_
    return (a + b) / 2, f((a + b) / 2)

min_t, _ = golden_search(func, -3, 5)

5. **数值优化库** (如Scipy的`minimize`):

from scipy.optimize import minimize

def optimize_min(f, bounds):
    result = minimize(f, x0=[2], method='SLSQP', bounds=bounds, options={'xtol': 0.01})
    return result.x[0], result.fun

min_t, _ = optimize_min(lambda t: t**3 - 2*t + 1, ((-3, 5),))

上述代码中，每种方法都需要根据具体情况调整初始猜测、学习率等参数。运行完成后，`min_t`就是找到的最小值对应的 `t` 值。