Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions

Hui Cao, Sergei V. Pereverzyev, Ian H. Sloan and Pavlo Tkachenko

Applied Mathematics and Computation, 2016, vol. 273, issue C, 993-1005

Abstract: In this paper, a two-step regularization method is used to solve an ill-posed spherical pseudo-differential equation in the presence of noisy data. For the first step of regularization we approximate the data by means of a spherical polynomial that minimizes a functional with a penalty term consisting of the squared norm in a Sobolev space. The second step is a regularized collocation method. An error bound is obtained in the uniform norm, which is potentially smaller than that for either the noise reduction alone or the regularized collocation alone. We discuss an a posteriori parameter choice, and present some numerical experiments, which support the claimed superiority of the two-step method.

Keywords: Two-parameter regularization; Spherical pseudo-differential equations; Quasi-optimality criterion (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315014046
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:993-1005

DOI: 10.1016/j.amc.2015.10.053

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().