Preconditioning rectangular spectral collocation
Numerical Analysis
2015-10-22 v2
Abstract
Rectangular spectral collocation (RSC) methods have recently been proposed to solve linear and nonlinear differential equations with general boundary conditions and/or other constraints. The involved linear systems in RSC become extremely ill-conditioned as the number of collocation points increases. By introducing suitable Birkhoff-type interpolation problems, we present pseudospectral integration preconditioning matrices for the ill-conditioned linear systems in RSC. The condition numbers of the preconditioned linear systems are independent of the number of collocation points. Numerical examples are given.
Keywords
Cite
@article{arxiv.1510.00195,
title = {Preconditioning rectangular spectral collocation},
author = {Kui Du},
journal= {arXiv preprint arXiv:1510.00195},
year = {2015}
}
Comments
12 pages, 2 figures