Conditioning moments of singular measures for entropy maximization II: Numerical examples. (English) Zbl 1351.30018
Hardin, Douglas P. (ed.) et al., Modern trends in constructive function theory. Constructive functions 2014 conference in honor of Ed Saff’s 70th birthday, Vanderbilt University, Nashville, TN, USA, May 26–30, 2014. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2534-0/pbk; 978-1-4704-2934-8/ebook). Contemporary Mathematics 661, 283-297 (2016).
Summary: If moments of singular measures are passed as inputs to the entropy
maximization procedure, the optimization algorithm might not terminate. The
framework developed in [M. Budišić and M. Putinar, Indag. Math., New Ser. 23, No. 4, 848–883 (2012; Zbl 1261.49012)] demonstrated how input moments of measures, on
a broad range of domains, can be conditioned to ensure convergence of the
entropy maximization. Here we numerically illustrate the developed framework
on simplest possible examples: measures with one-dimensional, bounded
supports. Three examples of measures are used to numerically compare approximations
obtained through entropy maximization with and without the
conditioning step.
For the entire collection see [Zbl 1343.00038].
For the entire collection see [Zbl 1343.00038].
MSC:
| 30E05 | Moment problems and interpolation problems in the complex plane |
| 30E20 | Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane |
| 41A46 | Approximation by arbitrary nonlinear expressions; widths and entropy |
