eqsolver - A Equation Solver library for Rust

This is a work-in-progress Rust Library aimed at applying Numerical Methods to solve Equations of all sorts. Currently the library provides way to find roots for function of single and multiple variables as well as minimizing norm of multivariate functions using Gauss-Newton.

Single Variable

There are 2 types of root-finders for single variable functions. Secant Method and Newton-Raphson's method, in which the latter can either be given the derivative of the function if available or the function can be approximated using finite differences.

Example of Newton-Raphson's method with finite differences. ```rust use eqsolver::solvers::single_variable::FDNewton;

let f = |x: f64| x.exp() - 1./x; // e^x = 1/x let solution = FDNewton::new(f).solve(0.5); // Starting guess is 0.5 ```

Multivariate Functions

There are 1 root-finder for multivariate methods and that is the Newton-Raphson method for system of equations. There also is the Gauss-Newton method that given its input it minimizes (in a least square manner) the square of the norm of the function represneting the system of equation. Both Newton-Raphson and Gauss-Newton have a version in which the Jacobian can be explicitly passed in or a version which it can be approximated using finite differences.

This part is heavily built using The Linear Algebra Library for Rust nalgebra.

Example of Newton-Raphson's method for system of equations ```rust use eqsolver::solvers::multivariable::MultiVarNewton; use nalgebra::{Vector2, Matrix2}; // Want to solve x^2 - y = 1 and xy = 2 let F = |v: Vector2| Vector2::new(v[0].powi(2) - v[1] - 1., v[0] * v[1] - 2.);

// Jacobian of F let J = |v: Vector2| Matrix2::new(2. * v[0], -1., v[1], v[0]);

let solution = MultiVarNewton::new(F, J).solve(Vector2::new(1., 1.)); ```

Planning