A stochastic Levenberg-Marquardt method using random models with complexity results and application to data assimilation

Globally convergent variants of the Gauss-Newton algorithm are often the methods of choice to tackle nonlinear least-squares problems. Among such frameworks, Levenberg-Marquardt and trust-region methods are two well-established, similar paradigms. Both schemes have been studied when the Gauss-Newton model is replaced by a random model that is only accurate with a given probability. Trust-region schemes … Read more

Do You Trust Derivatives or Differences?

We analyze the relationship between the noise level of a function and the accuracy and reliability of derivatives and difference estimates. We derive and empirically validate measures of quality for both derivatives and difference estimates. Using these measures, we quantify the accuracy of derivatives and differences in terms of the noise level of the function. … Read more