Research

My research program concerns the analysis of nonlinear solvers and their applications. The topic of my dissertation was the analysis and implementation of Anderson acceleration to Newton’s method. This work lead to two publications which are summarized here.

Lately, my energy has been devoted to generalizing theoretical results concerning Anderson acceleration applied to Newton-like methods, and stuyding gamma-safeguarding. This was a safeguarding scheme introduced in [1], and generalized in [2], to obtain a local convergence result for Anderson accelerated Newton’s method. Rather than simply a theoretical tool, numerical results in [2] indicate the potential for adaptive gamma-safeguarded Anderson to be a viable method in its own right.