A unified theory of strong uniqueness in uniform approximation with constraints

Chalmers, Bruce L.; Taylor, G. D.

doi:10.1016/0021-9045(83)90114-4

“…From a qualitative standpoint, this method may be said to provide us with an alternative route towards this strong uniqueness property, essentially different from the usual non‐constructive one taken e.g. by [1, 15].…”

Section: Further Remarksmentioning

confidence: 99%

Bounds on strong unicity for Chebyshev approximation with bounded coefficients

Sipoş

¹

2021

Mathematische Nachrichten

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We obtain new effective results in best approximation theory, specifically moduli of uniqueness and constants of strong unicity, for the problem of best uniform approximation with bounded coefficients, as first considered by Roulier and Taylor. We make use of techniques from the field of proof mining, as introduced by Kohlenbach in the 1990s. In addition, some bounds are obtained via the Lagrangian interpolation formula as extended through the use of Schur polynomials to cover the case when certain coefficients are restricted to be zero.

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“…From a qualitative standpoint, this method may be said to provide us with an alternative route towards this strong uniqueness property, essentially different from the usual non-constructive one taken e.g. by [1,14]. If we do not care about linearity, one may improve the modulus obtained above by removing its dependence on a lower bound for E, as shown by the following proposition.…”

mentioning

confidence: 99%

Bounds on strong unicity for Chebyshev approximation with bounded coefficients

Sipos

2019

Preprint

0

View full text Add to dashboard Cite

We obtain new effective results in best approximation theory, specifically moduli of uniqueness and constants of strong unicity, for the problem of best uniform approximation with bounded coefficients, as first considered by Roulier and Taylor. We make use of techniques from the field of proof mining, as introduced by Kohlenbach in the 1990s. In addition, some bounds are obtained via the Lagrangian interpolation formula as extended through the use of Schur polynomials to cover the case when certain coefficients are restricted to be zero.

show abstract