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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Computation of capacity


Authors: Thomas Ransford and Jérémie Rostand
Journal: Math. Comp. 76 (2007), 1499-1520
MSC (2000): Primary 65E05; Secondary 31A15, 90C05
Published electronically: January 24, 2007
MathSciNet review: 2299786
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Abstract: This article introduces a method for computing upper and lower bounds for the logarithmic capacity of a compact plane set. If the set has the Hölder continuity property, then these bounds converge to the value of the capacity. A number of examples are discussed in detail, including the Cantor middle-third set, for which we estimate $ c(E)\approx0.220949102189507$.


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Additional Information

Thomas Ransford
Affiliation: Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4
Email: ransford@mat.ulaval.ca

Jérémie Rostand
Affiliation: Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4
Email: jrostand@mat.ulaval.ca

DOI: http://dx.doi.org/10.1090/S0025-5718-07-01941-2
PII: S 0025-5718(07)01941-2
Keywords: Capacity, matrix game, H\"older continuity property, Cantor set
Received by editor(s): January 18, 2005
Received by editor(s) in revised form: July 6, 2005
Published electronically: January 24, 2007
Additional Notes: The first author was supported by grants from NSERC and the Canada Research Chairs program
The second author was supported by a grant from NSERC
Article copyright: © Copyright 2007 American Mathematical Society