We will make a link between the steepest descent method for an unconstrained minimisation problem and fixed-point iterations for its Euler-Lagrange equation. In this context, we shall rediscover the preconditioned nonlinear conjugate gradient method for the discretised problem. The benefit of the link between the two methods will be illustrated by a numerical experiment.

翻译：我们将在未受限制的最小化问题最陡峭的下降方法与其欧拉-拉格朗等式的固定点迭代之间建立联系。 在这方面,我们将重新发现这个分解问题的前提性非线性同化梯度方法。 数字实验将说明这两种方法之间联系的好处。