A stability analysis of the harmonic continuation
Elcrat, Alan R. Isakov, Victor Kropf, Everett Stewart, Darrell Anne
Elcrat, Alan R.
Isakov, Victor
Kropf, Everett
Stewart, Darrell Anne
Citations
Altmetric:
Other Names
Location
Time Period
Advisors
Original Date
Digitization Date
Issue Date
2012-07
Type
Article
Genre
Keywords
Mathematical physics
Subjects (LCSH)
Citation
A. Elcrat, V. Isakov, E. Kropf and D Stewart. 2012. A stability analysis of the harmonic continuation.INVERSE PROBLEMS, 28 (7):10.1088/0266-5611/28/7/075016 JUL 2012
Abstract
We consider the Cauchy problem for harmonic functions outside some disc
in the plane with the Cauchy data on an interval. We obtain simple formulae
for singular values of the operator solving this Cauchy problem and explicit
bounds on the difference between the exact and truncated operators. For a
typical particular geometry we compute numerically these singular values and
analyse their dependence on the size of the interval, on its distance to the
disc, etc. As a consequence, we can tell how many parameters of the harmonic
function (or of a source producing this function) can be found from the Cauchy
data.
Table of Contents
Description
Click on the DOI link below to access this article (may not be free)
Publisher
IOP PUBLISHING LTD
Journal
Book Title
Series
INVERSE PROBLEMS; 2012, v.28, no.7
Digital Collection
Finding Aid URL
Use and Reproduction
Archival Collection
PubMed ID
DOI
ISSN
0266-5611