We consider the problem of numerically identifying roots of a target function - under the constraint that we can only measure the derivatives of the function at a given point, not the function itself. We describe and characterize two methods for doing this: (1) a local-inversion "inching process", where we use local measurements to repeatedly identify approximately how far we need to move to drop the target function by the initial value over N, an input parameter, and (2) an approximate Newton's method, where we estimate the current function value at a given iteration via estimation of the integral of the function's derivative, using N samples. When applicable, both methods converge algebraically with N, with the power of convergence increasing with the number of derivatives applied in the analysis.

翻译：我们考虑从数字上确定目标函数的根基问题,因为我们只能测量该函数在某一点的衍生物,而不是函数本身。我们描述和定性两种方法来做到这一点:(1) 本地反转“加速过程”,我们用当地测量方法反复确定我们距离目标函数的初始值比N(输入参数)要下降大约多远,以及(2) 牛顿的近似方法,我们用N样本估算函数衍生物的有机成分,从而估计特定迭代时的当前函数值。在适用的情况下,这两种方法都与N相交,与分析中应用的衍生物的趋同力不断增加。</s>