Date of Award

Spring 2015

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computer Science

First Advisor

Ahmed Sameh

Committee Chair

Ahmed Sameh

Committee Member 1

Ananth Grama

Committee Member 2

Alex Pothen

Committee Member 3

Robert Skeel

Committee Member 4

Rudolf Eigenmann

Abstract

Sparse symmetric eigenvalue problems arise in many computational science and engineering applications: in structural mechanics, nanoelectronics, and spectral reordering, for example. Often, the large size of these problems requires the development of eigensolvers that scale well on parallel computing platforms. In this dissertation, we describe two such eigensolvers, TraceMin and TraceMin-Davidson. These methods are different from many other eigensolvers in that they do not require accurate linear solves to be performed at each iteration in order to find the smallest eigenvalues and their associated eigenvectors. After introducing these closely related eigensolvers, we discuss alternative methods for solving the saddle point problems arising at each iteration, which can improve the overall running time. Additionally, we present TraceMin-Multisectioning, a new TraceMin implementation geared towards finding large numbers of eigenpairs in any given interval of the spectrum. We conclude with numerical experiments comparing our trace-minimization solvers to other popular eigensolvers (such as Krylov-Schur, LOBPCG, Jacobi-Davidson, and FEAST), establishing the competitiveness of our methods.

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