Numerical Analysis Algorithms in Julia

Welcome to the Numerical Analysis Algorithms repository in Julia! This repository hosts a collection of efficient algorithms for numerical analysis tasks, specifically focusing on finding zeros/fixed points of functions and data interpolation.

Features

• Zero Finding Algorithms: Implementations of various methods for finding zeros and fixed points of functions, including but not limited to:
  • Bisection method
  • Newton-Raphson method
  • Secant method
  • Fixed-point iteration method
• Interpolation Techniques: Tools for interpolating data using methods such as:
  • Linear interpolation
  • Polynomial interpolation (Lagrange, Newton)

Getting Started

To get started with using the algorithms in this repository, follow these steps:

1. Clone the repository to your local machine:

   git clone https://github.com/CasuallyPassingBy/NumAlgoJulia.git

2. Navigate to the repository directory:

    cd NumAlgoJulia

3. Explore the src directory to find the implementations of the numerical analysis algorithms.

Use the algorithms in your Julia projects by importing the necessary modules.

Usage

Here's a basic example demonstrating how to use the zero finding algorithms:

include("FindingZeros.jl")
import .Finding_Zeros
# Function you want to find the zero of
f(x) = x^2 - 2
#Find the approximate zero between 1 and 2 using the Bisection method
approx_zero = Finding_Zeros.bisection(f, 1, 2)

And here's how to perform linear interpolation on a dataset:

include("Interpolating.jl")
import .Interpolating
# Sample data points
x_values = [0, 1, 2, 3, 4]
y_values = [0, 1, 4, 9, 16]

# Interpolate at x = 2.5 using Neville's method
interp_value_neville = Interpolating.nevilles_method(x_values, y_values, 2.5)

Contributing

Contributions to this repository are welcome! If you have implemented additional numerical analysis algorithms or have suggestions for improvements, feel free to open an issue or submit a pull request.

License

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