README.md

GMRES: Generalized minimum residual method

A sparse linear system solver using the GMRES iterative method.

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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

use gmres;
use rsparse::data::Sprs;

fn main() {
    // Define an arbitrary matrix `A`
    let a = 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,
    );
}