4 papers
Random Walks, Faber Polynomials and Accelerated Power Methods
Peter Cowal, Nicholas F. Marshall, Sara Pollock
In this paper, we construct families of polynomials defined by recurrence relations related to mean-zero random walks. We show these families of polynomials can be used to approxim…
Momentum accelerated power iterations and the restarted Lanczos method
Alessandro Barletta, Nicholas Marshall, Sara Pollock
In this paper we compare two methods for finding extremal eigenvalues and eigenvectors: the restarted Lanczos method and momentum accelerated power iterations. The convergence of b…
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…
Faber polynomials in a deltoid region and power iteration momentum methods
Peter Cowal, Nicholas F. Marshall, Sara Pollock
We consider a region in the complex plane enclosed by a deltoid curve inscribed in the unit circle, and define a family of polynomials that satisfy the same recurrence relati…