# Crate gmres

Expand description

## §GMRES: Generalized minimum residual method

A sparse linear system solver using the GMRES iterative method.

This crates provides a solver for `Ax=b` linear problems using the GMRES method. Sparse matrices are a common representation for many real-world problems commonly found in engineering and scientific applications. This implementation of the GMRES method is specifically tailored to sparse matrices, making it an efficient and effective tool for solving large linear systems arising from real-world problems.

### §Example:

#### §Solve a linear system

``````// Define an arbitrary matrix `A`
let a = rsparse::data::Sprs::new_from_vec(&[
vec![0.888641, 0.477151, 0.764081, 0.244348, 0.662542],
vec![0.695741, 0.991383, 0.800932, 0.089616, 0.250400],
vec![0.149974, 0.584978, 0.937576, 0.870798, 0.990016],
vec![0.429292, 0.459984, 0.056629, 0.567589, 0.048561],
vec![0.454428, 0.253192, 0.173598, 0.321640, 0.632031],
]);

// Define a vector `b`
let b = vec![0.104594, 0.437549, 0.040264, 0.298842, 0.254451];

// Provide an initial guess
let mut x = vec![0.; b.len()];

// Solve for `x`
gmres::gmres(&a, &b, &mut x, 100, 1e-5).unwrap();

// Check if the result is correct
gmres::test_utils::assert_eq_f_vec(
&x,
&vec![0.037919, 0.888551, -0.657575, -0.181680, 0.292447],
1e-5,
);``````

## Functions§

• GMRES solver for `Sprs` input matrices. Solves Ax = b. Overwrites x with the solution.