如何计算 $\frac{\sqrt{5} - 1}{2}$ ?

• 特征值分解

  \(x^2 - x - 1 = 0\)

• 移项，除以x，求x的非零解

  \(x = 1 + \frac{1}{x}, x = 1 + \frac{1}{1 + \frac{1}{1 + ...}}\)

• 迭代

  \(x_{n + 1} = 1 + \frac{1}{x_n}\)
  \(x_0 = 1\)