中文摘要：

概要地介绍了在非启发式非线性反演方法——共轭梯度法的原理、算法、优点，以及它的局限性，和改进型算法：一种全局收敛的随机共轭梯度法。最后通过一个例子来说明共轭梯度法及其改进型算法的优缺点。

英文摘要：

This paper briefly introduces a non- heuristic and non- linear inverse method -- Conjugate Gradient Method, including its principle, algorithm, advantages and limitation, also introduces a method Stochastic Conjugate Gradient Method which is an improvement of traditional CG, a globally convergence and hybrid algorithm with stochastic hillclimbing technique. At last, a numerical test is given to show some advantages and disadvantages of Conjugate Gradient Method compared with Stochastic Conjugate Gradient Method.