Pointwise convergence of Jacobi polynomials

Thumbnail Image

Files

master_Kruglov_Ekaterina_2018.pdf (1.43 MB)

URL

Journal Title

Journal ISSN

Volume Title

Perustieteiden korkeakoulu | Master's thesis
Unless otherwise stated, all rights belong to the author. You may download, display and print this publication for Your own personal use. Commercial use is prohibited.

Authors

Date

2018-05-08

Department

Major/Subject

Applied Mathematics

Mcode

SCI3053

Degree programme

Master’s Programme in Applied and Engineering Mathematics (N5TeAM)

Language

en

Pages

48

Series

Abstract

The goal of this thesis is to numerically study a pointwise Jacobi convergence theorem for piecewise analytic functions based on the theorem on Legendre error. The convergence rates were examined on the boundary, singularity, and interior points. Results revealed that pointwise error convergence rates depend on the point of singularity, Jacobi polynomial coefficients α and β, and, lastly, on type of the piecewise analytic function.

Description

Supervisor

Hakula, Harri

Thesis advisor

Hanke, Michael

Keywords

Jacobi polynomials, pointwise convergence, orthogonal polynomials, Gibbs phenomenon, approximation theory

Other note

Citation

Permanent link to this item

https://urn.fi/URN:NBN:fi:aalto-201806012999

Collections

[dipl] Perustieteiden korkeakoulu / SCI