 Can a semi-simple eigenvalue admit fractional sensitivities?A. Luongo and M. Ferretti Applied Mathematics and Computation, 2015, vol. 255, issue C, 165-178 Abstract: We perform high-order sensitivity analysis of eigenvalues and eigenvectors of linear systems depending on parameters. Attention is focused on double not-semi-simple and semi-simple eigenvalues, undergoing perturbations, either of regular or singular type. The use of integer (Taylor) or fractional (Puiseux) series expansions is discussed, and the analysis carried out both on the characteristic polynomial and on the eigenvalue problem. It is shown that semi-simple eigenvalues can admit fractional sensitivities when the perturbations are singular, conversely to the not-semi-simple case. However, such occurrence only manifests itself when a second-order perturbation analysis is carried out. As a main result, it is found that such over-degenerate case spontaneously emerges in bifurcation analysis, when one looks for the boundaries of the stability domain of circulatory mechanical systems possessing symmetries. A four degree-of-freedom system under a follower force is studied as an illustrative example. Keywords: Sensitivity analysis; Semi-simple eigenvalue; Singular perturbations; Stability domain; Circulatory systems (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:255:y:2015:i:c:p:165-178 DOI: 10.1016/j.amc.2014.01.178 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.