Optimal error estimates for Chebyshev approximations of functions with limited regularity in fractional Sobolev-type spaces. (English) Zbl 1428.41020
In this paper, there are introduced a new framework of fractional Sobolev-type spaces. The authors focused on the Chebyshev approximation but the analysis techniques are extendable to general Jacobi approximations. They put emphasis on estimating the decay rate of expansion coefficients for the reason that the errors of spectral expansions in various norms, and the related interpolation and quadratures, can be estimated directly from the sums of the coefficients.
Reviewer: Włodzimierz Łenski (Poznań)
MSC:
| 41A25 | Rate of convergence, degree of approximation |
| 41A10 | Approximation by polynomials |
| 41A50 | Best approximation, Chebyshev systems |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
approximation by Chebyshev polynomials; fractional integrals/derivatives; fractional Sobolev-type spaces; singular functions; optimal estimatesSoftware:
DLMFReferences:
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