Fitting functions of Jackson type for three-dimensional data

ABSTRACT

We study some procedures for the approximation of three-dimensional data on a grid with a hypothesis of periodicity. The first part proposes a generalization of a discrete periodic approximation defined by Dunham Jackson. The functions used have the advantage of owning an analytical explicit expression in terms of the samples (specific values) of the original function or data. In the second part, we describe a continuous approximation function for the same problem, defined through an integral. Some results of the rate of convergence and bounds of the approximation error are presented, with the single hypothesis of Hölder continuity or continuity of the original function.

KEYWORDS:

• Trigonometric approximation
• trigonometric interpolation
• smoothing
• surface fitting
• approximation on torus

2000 AMS SUBJECT CLASSIFICATIONS:

• 42A10
• 42A15
• 42A05
• 65D10
• 65D05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been partially supported by the Projects: CUD-ID: 2013-05 and CUD-ID: 2015-05 of the Ministerio de Defensa (Spain).