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Related Experiment Video

Updated: Jan 28, 2026

Operation of a Benchtop Bioreactor

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Published on: September 12, 2013

On Shepard-Gupta-type operators.

Umberto Amato¹, Biancamaria Della Vecchia²

¹1Consiglio Nazionale delle Ricerche, Istituto per la Microelettronica e Microsistemi, Napoli, Italy.

Journal of Inequalities and Applications

|March 7, 2019

Summary

This summary is machine-generated.

Researchers introduced a new Gupta-type variant of Shepard operators, providing convergence and approximation results. This variant improves a previous algorithm for image compression applications.

Keywords:

Direct and converse results Gupta-type variant Image compression Shepard operators

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Area of Science:

Approximation Theory
Numerical Analysis

Background:

Shepard operators are fundamental in approximation theory.
Existing variants have limitations in certain applications.

Purpose of the Study:

Introduce a novel Gupta-type variant of Shepard operators.
Analyze its approximation properties and convergence.
Explore its application in image compression.

Main Methods:

Construction of the Gupta-type Shepard operators.
Theoretical analysis of convergence and approximation error bounds (pointwise and uniform).
Implementation and evaluation in an image compression algorithm.

Main Results:

Established convergence theorems for the new operators.
Derived direct and converse approximation theorems.
Demonstrated improved performance in image compression compared to previous methods.

Conclusions:

The Gupta-type Shepard operators offer enhanced approximation capabilities.
The proposed variant shows practical utility in image compression.
Further research can explore generalizations and other applications.