Module krylov 

Krylov subspace methods for solving linear equations with abstract tensors.

This module provides iterative solvers that work with any type implementing TensorLike, enabling their use in tensor network algorithms without requiring dense vector representations.

Solvers

• gmres: Generalized Minimal Residual Method (GMRES) for non-symmetric systems

Future Extensions

• CG (Conjugate Gradient) for symmetric positive definite systems
• BiCGSTAB for non-symmetric systems with better convergence properties

Example

use tensor4all_core::krylov::{gmres, GmresOptions};

// Define a linear operator as a closure
let apply_operator = |x: &T| -> Result<T> {
    // Apply your linear operator to x
    operator.apply(x)
};

let result = gmres(&apply_operator, &rhs, &initial_guess, &GmresOptions::default())?;

Structs

GmresOptions

Options for GMRES solver.

GmresResult

Result of GMRES solver.

RestartGmresOptions

Options for restarted GMRES with truncation.

RestartGmresResult

Result of restarted GMRES solver.

Functions

gmres

Solve A x = b using GMRES (Generalized Minimal Residual Method).

gmres_with_truncation

Solve A x = b using GMRES with optional truncation after each iteration.

restart_gmres_with_truncation

Solve A x = b using restarted GMRES with truncation.