Dissertation/Thesis Abstract

Variations of the FEAST eigenvalue algorithm
by Kajpust, Stephanie, M.S., Michigan Technological University, 2014, 130; 1557412
Abstract (Summary)

FEAST is a recently developed eigenvalue algorithm which computes selected interior eigenvalues of real symmetric matrices. It uses contour integral resolvent based projections. A weakness is that the existing algorithm relies on accurate reasoned estimates of the number of eigenvalues within the contour. Examining the singular values of the projections on moderately-sized, randomly-generated test problems motivates orthogonalization-based improvements to the algorithm. The singular value distributions provide experimentally robust estimates of the number of eigenvalues within the contour. The algorithm is modified to handle both Hermitian and general complex matrices. The original algorithm (based on circular contours and Gauss-Legendre quadrature) is extended to contours and quadrature schemes that are recursively subdividable. A general complex recursive algorithm is implemented on rectangular and diamond contours. The accuracy of different quadrature schemes for various contours is investigated.

Indexing (document details)
Advisor: Struthers, Allan
Commitee: Ott, Linda, Schmitz, Rebecca, Sun, Jiguang
School: Michigan Technological University
Department: Mathematical Sciences
School Location: United States -- Michigan
Source: MAI 53/02M(E), Masters Abstracts International
Subjects: Mathematics
Keywords: Algorithm, Complex, Eigenvalues, Quadrature
Publication Number: 1557412
ISBN: 9781303947858
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