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Abstract: In this
thesis we consider unsmoothed aggregation algebraic multigrid preconditioners applied to
graph ranking problems arising from the HodgeRank algorithm. We will discuss the
HodgeRank algorithm's foundations after a brief discussion of common ranking methods and
present an analysis of the UA-AMG method for solving graph Laplacians systems arising
from the least squares ... read moreproblems,applying it as a preconditioner for conjugate gradient
(CG) to achieve better performance. We also provide experiments comparing the LSRN,
LSQR, and CG method (with and without UA-AMG as a preconditoner) on a collection of
larger random graphs and a collection of real world network topologies to demonstrate
the effectiveness of UA-AMG method for solving least squares problems on
graphs.
Thesis (M.S.)--Tufts University,
2018.
Submitted to the Dept. of Computer
Science.
Advisor: Shuchin
Aeron.
Committee: Xiaozhe Hu, and Misha
Kilmer.
Keywords: Applied mathematics, and Computer
science.read less
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