Overview

This Rust program calculates the Lagrange interpolation polynomial from a set of given points. Lagrange interpolation is a method of constructing a polynomial that passes through a set of known points.

Features

• Lagrange Polynomial Calculation: Given a set of points, the program constructs the Lagrange interpolation polynomial that passes through all those points.
• Polynomial Operations: The program supports polynomial addition, multiplication, and scaling.
• Formatted Output: The final interpolated polynomial is displayed in standard algebraic form.

How it Works

Given a set of $n + 1$ distinct points $(x_0, y_0), (x_1, y_1), \ldots, (x_n, y_n)$, the Lagrange interpolating polynomial $P(x)$ is defined as: $$P(x) =\sum_{i=0}^{n} y_i L_i(x)$$ where $L_i(x)$ are the Lagrange basis polynomials, defined as: $$L_i(x) = \prod\limits_{{0 \leq j \leq n}_{j \neq i}} \frac{x - x_j}{x_i - x_j}$$

Example

• Given the points $(0,4), (−2,1)$, and $(2,3)$, the program computes the interpolated polynomial.

Example Output

The interpolated polynomial is: 0.33x^2 + 0.83x + 4.00

Requirements

• Rust installed on your machine. (If Rust is not installed, follow the instructions on the official Rust website to install it).

Contributing

• If you intend to contribute to this project, fork the repository and make a pull request.

Usage

• To use this code, you can clone or download this repository.
• Compile and run the Rust program using the following command:

cargo build
cargo run

Acknowledgments

• Rust

Clone the repository:

git clone /~https://github.com/cypriansakwa/Lagrange_Interpolation_Polynomial_from_Given_Points_in_Rust.git
cd Lagrange_Interpolation_Polynomial_from_Given_Points_in_Rust