Skip to Main content Skip to Navigation
Journal articles

Determining Projection Constants of Univariate Polynomial Spaces

Abstract : The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a linear program, and the lower bound, produced by a semidefinite program exploiting the method of moments, are often close enough to deduce the projection constant with reasonable accuracy. The implementation of these programs makes it possible to find the projection constant of several three-dimensional spaces with five digits of accuracy, as well as the projection constants of the spaces of cubic, quartic, and quintic polynomials with four digits of accuracy. Beliefs about uniqueness and shape-preservation of minimal projections are contested along the way.
Complete list of metadata

Cited literature [14 references]  Display  Hide  Download

https://hal.laas.fr/hal-01679124
Contributor : Jean Bernard Lasserre <>
Submitted on : Friday, January 12, 2018 - 10:41:29 AM
Last modification on : Thursday, June 10, 2021 - 3:07:05 AM

Files

GMPforMP_v77.pdf
Files produced by the author(s)

Identifiers

Citation

Simon Foucart, Jean-Bernard Lasserre. Determining Projection Constants of Univariate Polynomial Spaces. Journal of Approximation Theory, Elsevier, 2018, 235, pp.74-91. ⟨10.1016/j.jat.2018.06.002⟩. ⟨hal-01679124⟩

Share

Metrics

Record views

320

Files downloads

288