The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Construction of polygonal interpolants: a maximum entropy approach
Abstract
In this paper, we establish a link between maximizing (information‐theoretic) entropy and the construction of polygonal interpolants. The determination of shape functions on n‐gons (n>3) leads to a non‐unique under‐determined system of linear equations. The barycentric co‐ordinates ϕi, which form a partition of unity, are associated with discrete probability measures, and the linear reproducing conditions are the counterpart of the expectations of a linear function. The ϕi are computed by maximizing the uncertainty H(ϕ 1,ϕ 2,…,ϕn)=−∑ ϕi logϕi, subject to the above constraints. The description is expository in nature, and the numerical results via the maximum entropy (MAXENT) formulation are compared to those obtained from a few distinct polygonal interpolants. The maximum entropy formulation leads to a feasible solution for ϕi in any convex or non‐convex polygon. This study is an instance of the application of the maximum entropy principle, wherein least‐biased inference is made on the basis of incomplete information. Copyright © 2004 John Wiley & Sons, Ltd.
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Cites
A Mathematical Theory of Communication
Shannon, C. E. (1948) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1948.tb01338.x · Cited by 88,486
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On the rationale of maximum-entropy methods
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Metadata
- Authors
- Sukumar, N.
- Venue
- International Journal for Numerical Methods in Engineering
- Publisher
- Wiley
- Published
- 2004-11-15
- Volume
- 61
- Issue
- 12
- Pages
- 2159-2181
- ISSN
- 0029-5981 (ISSN-L)
- 1097-0207
- OpenAlex
- W1968819696
- Cited by
- 274
- References
- 14
- FWCI
- 5.19
- Type
- journal article
- Language
- en
- Open access
- closed
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