Date of Award
2014
Document Type
Master's Thesis
Degree Name
Master of Science in Mathematical Sciences (MS)
College, School or Department Name
Department of Mathematical Sciences
Advisor
Allen Struthers
Abstract
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.
Recommended Citation
Kajpust, Stephanie, "Variations of the FEAST Eigenvalue Algorithm", Master's Thesis, Michigan Technological University, 2014.