Numerical Interpolation

A Java project for performing numerical interpolations, featuring implementations of Lagrangian polynomial interpolation, linear spline interpolation, and cubic spline interpolation.

Features

• Polynomial: A complete Polynomial management module.
• Lagrangian Polynomial Interpolation: Estimate values between known data points using polynomials.
• Linear Spline Interpolation: Piecewise linear approach ensuring continuity.
• Cubic Spline Interpolation: Piecewise cubic polynomial approach providing smoother transitions.
• Integration Error: Provide a method to evaluate interpolations error.

Getting Started

Prerequisites

• Java Development Kit (JDK) installed on your system. (version >= 17)

Installation

Clone this repository:

git clone https://github.com/igorgreenigm/interpolation.git

Navigate to the project directory:

cd interpolation

You can compile directly the Java files:

javac src/*.java

Or, Open project with intelliJ IDE or directly import classes in your own project.

Usage

To use this library in your project, include the provided classes. Detailed usage instructions and examples are available in the code comments.

The function $f$ used in the interpolation examples is defined as: $f(x) = \frac{1}{1 + 25x^2}$

All interpolations

Lagrangian + Tchebyshev interpolations

Errors by interpolation

Error is computed using the formula $\sqrt{\int_a^b \left( f(x) - p(x) \right)^2dx}$ :

• $f$ is the function to interpolate.
• $p$ the interpolation polynomial (or set of polynomial for splines).
• $[a, b]$ is the interval of distibuted samples.

Contributing

• IgorGreenIGM
• Willy Watcho
• Oliver Mokiage
• Natacha Fonkou
• Audrey Mbeuyo
• @FTZ

License

This project is licensed under the MIT License - see the LICENSE file for details.