NumeriXCore

NumeriXCore is a high-performance numerical analysis library designed for various scientific and engineering applications. This library is implemented in C++ and can be compiled to WebAssembly using Emscripten, making it suitable for both native and web-based applications.

Features

• Iterative Methods for Solving Equations
• Solutions of Systems of Linear Equations
• Handling of Special Matrices
• Solutions for Simultaneous Nonlinear Equations
• Computation of Eigenvalues and Eigenvectors
• Polynomial Interpolation and Approximation
• Numerical Integration Techniques
• Solutions to Initial and Boundary Value Problems for ODEs
• Finite Element Method

Getting Started

Prerequisites

• C++17 or higher
• CMake 3.0 or higher
• Emscripten (for WebAssembly build)

Building the Library

1. Clone the repository:

   git clone https://github.com/PhlyingPhalanges/NumeriXCore.git
   cd NumeriXCore

2. Create a build directory and navigate into it:

   mkdir build
   cd build

3. Run CMake to configure the project:

   cmake ..

4. Build the project:

   make

Building for WebAssembly

1. Install Emscripten: Follow the instructions on the Emscripten website.

2. Activate the Emscripten environment:

   source /path/to/emsdk/emsdk_env.sh

3. Create a build directory and navigate into it:

   mkdir build
   cd build

4. Run CMake with Emscripten toolchain:

   emcmake cmake ..

5. Build the project:

   emmake make

Usage

Include the NumeriXCore library in your project and link it during the build process. Here is a simple example:

C++

#include <iostream>
#include "iterative_methods.hpp"

int main() {
    // Example usage of the library
    double result = simple_iteration([](double x) { return cos(x); }, 1.0, 1e-6);
    std::cout << "Root: " << result << std::endl;
    return 0;
}

Acknowledgements

This library was developed with insights gained from various textbooks and academic resources on numerical analysis. Key references that informed the principles and methods applied in this library include:

• Süli, E., & Mayers, D. F. (2003). An Introduction to Numerical Analysis. Cambridge: Cambridge University Press.
• Another APA citation here once I find one

These resources provided a solid foundation in numerical methods, which was instrumental in the development of NumeriXCore.