Computation of capacity
Authors:
Thomas Ransford and Jérémie Rostand
Journal:
Math. Comp. 76 (2007), 1499-1520
MSC (2000):
Primary 65E05; Secondary 31A15, 90C05
DOI:
https://doi.org/10.1090/S0025-5718-07-01941-2
Published electronically:
January 24, 2007
MathSciNet review:
2299786
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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 $c(E)\approx 0.220949102189507$.
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Additional Information
Thomas Ransford
Affiliation:
Département de mathématiques et de statistique, Université Laval, Québec (QC), Canada G1K 7P4
MR Author ID:
204108
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
Keywords:
Capacity,
matrix game,
Hölder 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
