__Claremont Graduate University__ | __Claremont McKenna__ | __Harvey Mudd__ | __Pitzer__ | __Pomona__ | __Scripps__

Proudly Serving Math Community at the Claremont Colleges Since 2007

Copyright © 2011 Claremont Center for the Mathematical Sciences

10/04/2016 - 12:15pm

10/04/2016 - 1:10pm

Speaker:

Anna Ma (CGU)

Abstract:

Stochastic iterative algorithms such as the Kacmarz and Gauss-Seidel methods have gained recent attention because of their speed, simplicity, and the ability to approximately solve large-scale linear systems of equations without needing to access the entire matrix. In this work, we consider the setting where we wish to solve a linear system in a large matrix X that is stored in a factorized form, $X = UV$; this setting either arises naturally in many applications or may be imposed when working with large low-rank datasets for reasons of space required for storage. We propose a variant of the randomized Kaczmarz method for such systems that takes advantage of the factored form, and avoids computing $X$. We prove an exponential convergence rate and supplement our theoretical guarantees with experimental evidence demonstrating that the factored variant yields significant acceleration in convergence.

Where:

Millikan 2099, Pomona College