Overview

This Rust program implements the Lagrange interpolation method to estimate the value of a function at a specific point, given a set of known points.

Features

• Lagrange Interpolation: Interpolates a value for a given $x$ based on a set of points.
• Flexible Input: You can modify the points and the target $x$ value to compute the interpolated result for different cases.
• Simple and Efficient: Implements the Lagrange formula in a straightforward and efficient manner using Rust.

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: $$L_i(x) = \prod\limits_{{0 \leq j \leq n}_{j \neq i}} \frac{x - x_j}{x_i - x_j}$$
• Given a set of known points, the program uses this formula to calculate the value of the interpolated polynomial at any given point $x$.

Example

• Given the points $(0,4), (−2,1)$, and $(2,3)$, this program computes the interpolated value for any $x$ you choose. For example, if $x=-2$, the output will show the value of the polynomial at that point.

Example Output

The interpolated value at x = -2 is: 1.0

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_of_Given_Points_in_Rust.git
cd Lagrange_Interpolation_of_Given_Points_in_Rust