@TechReport{ it:2018-012,
author = {Sven-Erik Ekstr{\"o}m and Stefano Serra-Capizzano},
title = {Eigenvalue Isogeometric Approximations Based on
{B}-splines: Tools and Results},
institution = {Department of Information Technology, Uppsala University},
department = {Division of Scientific Computing},
year = {2018},
number = {2018-012},
month = jul,
abstract = {In such a short note we consider the spectral analysis of
large matrices coming from the numerical approximation of
the eigenvalue problem \[ -(a(x)u'(x))'=\lambda b(x)
u(x),\quad\quad x\in (0,1), \] where $u(0)$ and $u(1)$ are
given, by using isogeometric methods based on B-splines. We
give precise estimates for the extremal eigenvalues and
global distributional results. The techniques involve
dyadic decomposition arguments, the GLT analysis, and basic
extrapolation methods.}
}