Generalized trigonometric interpolation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:354

Article; Proceedings Paper

Navascues, M. A.¹  Jha, Sangita²  Chand, A. K. B.²  Sebastian, M. V.³ 

[1] Univ Zaragoza, Dept Matemat Aplicada, Escuela Ingn & Arquitectura, Zaragoza 500018, Spain

[2] Indian Inst Technol Madras, Dept Math, Chennai 600036, Tamil Nadu, India

[3] Acad Gen Mil, Ctr Univ Def, Zaragoza 50090, Spain

关键词: Fractal interpolation;    Trigonometric interpolation;    Smoothing;    Curve fitting;   

DOI  :  10.1016/j.cam.2018.08.003

来源: Elsevier

【 摘 要 】

This article proposes a generalization of the Fourier interpolation formula, where a wider range of the basic trigonometric functions is considered. The extension of the procedure is done in two ways: adding an exponent to the maps involved, and considering a family of fractal functions that contains the standard case. The studied interpolation converges for every continuous function, for a large range of the nodal mappings chosen. The error of interpolation is bounded in two ways: one theorem studies the convergence for Holder continuous functions and other develops the case of merely continuous maps. The stability of the approximation procedure is proved as well. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free