18 citations · 18 across the 4 of their papers we have counts for
4 papers
An adaptive framework for first-order gradient methods
Xiaozhe Hu, Sara Pollock, Zhongqin Xue +1
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the st…
Dynamically accelerating the power iteration with momentum
Christian Austin, Sara Pollock, Yunrong Zhu
In this paper, we propose, analyze and demonstrate a dynamic momentum method to accelerate power and inverse power iterations with minimal computational overhead. The method can be…
Uniqueness of discrete solutions of nonmonotone PDEs without a globally fine mesh condition
Sara Pollock, Yunrong Zhu
Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theore…
Local Convergence of Adaptive Methods for Nonlinear Partial Differential Equations
Michael Holst, Gantumur Tsogtgerel, Yunrong Zhu
In this article we develop convergence theory for a general class of adaptive approximation algorithms for abstract nonlinear operator equations on Banach spaces, and use the theor…