Academic project made for analyzing the performance and effectiveness of selected interpolation methods. These ones mentioned below are using LU decomposition in order to calculate the linear systems.
There are two projects implemented:
- For calculating the solutions (C++)
- For displaying them (Python3)
To make it work, the user must open the first project that is written in C++ and provide some input. Once the process is finished, the second project made in Python must be launched. Then the user is asked to choose a solution from the list to display the results.
Alternatively called "polynomial interpolation" is the simplest one to code. The goal is to build a function that has a degree equal to the given points amount. However, increasing the number of nodes worsens the interpolation. It is a well-known effect called Runge's phenomenon.
A function made of fragments of the polynomials that are glued together. It is a remedy for Runge's phenomenon. Moreover, the quality of interpolation is excellent, but the downside is the complexity of operations to be performed.
Here you can see the Runge's phenomenon at the extremes.
The code is written in C++, compatible with version 17 and higher, and Python3.