Accession Number : ADA626022


Title :   Parallel Symmetric Eigenvalue Problem Solvers


Descriptive Note : Doctoral thesis


Corporate Author : PURDUE UNIV LAFAYETTE IN


Personal Author(s) : Klinvex, Alicia M


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a626022.pdf


Report Date : May 2015


Pagination or Media Count : 161


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, I 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, I discuss alternative methods for solving saddle point problems arising in each iteration, which can improve the overall running time. Additionally, I present TraceMin-Multisectioning, a new TraceMin implementation geared towards finding large numbers of eigenpairs in any interval of the spectrum. I conclude with numerical experiments comparing my trace-minimization solvers to other popular eigensolvers (such as Krylov-Schur, LOBPCG, Jacobi- Davidson, and FEAST), establishing the competitiveness of my methods.


Descriptors :   *EIGENVALUES , *LINEAR SYSTEMS , *PARALLEL PROCESSING , *SPARSE MATRIX , ACCURACY , APPROXIMATION(MATHEMATICS) , CONVERGENCE , EIGENVECTORS , ELECTRON TRANSPORT , EXPERIMENTAL DESIGN , HAMILTONIAN FUNCTIONS , LATTICE DYNAMICS , MATHEMATICAL FILTERS , NANOTECHNOLOGY , NUMERICAL METHODS AND PROCEDURES , PATTERNS , POTENTIAL ENERGY , PROBABILITY , SCALING FACTOR , SPECTRA , SYMMETRY , THESES


Subject Categories : Numerical Mathematics
      Operations Research


Distribution Statement : APPROVED FOR PUBLIC RELEASE