EXPLICIT FORM AND VISUALIZATION OF RUNGE'S APPROXIMATION THEOREM

• Main Author: THANIA - NIM: 10114030 , ELSA
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/26921
• Institution: Institut Teknologi Bandung

<p align="justify">The purpose of function approximation, whether real or complex valued function, is to find another function which has a simpler form and yet its values are close to the values of the original function. Some theorems had been found in regard to function approximation and one of them is Runge's Theorem which discusses about complex-valued function approximation. In Runge's Theorem, it is said that every holomorfic function in a neighborhood of a compact set can be approximated uniformly by rational functions whose singularities are in the complement of the compact set. Runge's Theorem guarantees the existence of the rational functions but the explicit form of the rational function itself is not given. By proving Runge's Theorem the explicit form of the rational function is obtained. Then some complex functions are choosen to be approximated by these rational functions. By studying the errors and the visualization which concept is a mapping from a point in the domain to a particular vector, it can be concluded that the sequence of rational functions constructed approximate the functions choosen.<p align="justify"> <br />