Struct AugmentedKrylov 

pub struct AugmentedKrylov { /* private fields */ }

Augmented Krylov subspace solver (augmented GMRES).

Overview

Given an augmentation subspace W (external knowledge vectors – e.g., from previous solves or approximate eigenvectors), solves A x = b in the space x_0 + span(W) + K_m(A, r_0).

The solver uses standard GMRES (Arnoldi + least-squares) for the Krylov portion, and incorporates augmentation vectors by projecting the residual onto the range of A*W before each GMRES cycle.

After convergence, an updated augmentation subspace is extracted from the last Krylov basis for use in subsequent solves.

Implementations

impl AugmentedKrylov

pub fn new(config: AugmentedKrylovConfig) -> Self

Create an AugmentedKrylov solver with the given configuration.

pub fn with_defaults() -> Self

Create with default configuration.

pub fn solve<F>( &self, matvec: F, b: &[f64], x0: Option<&[f64]>, augmentation: &[Vec<f64>], ) -> Result<AugmentedKrylovResult, SparseError>

where F: Fn(&[f64]) -> Vec<f64>,

Solve A x = b with augmented Krylov subspace.

Arguments

• matvec - Closure for the matrix-vector product y = A x.
• b - Right-hand side.
• x0 - Optional initial guess.
• augmentation - External vectors to augment the Krylov space. These are incorporated by projecting the residual onto span(A*W) at each restart. Pass an empty slice for standard (non-augmented) GMRES.

Returns

An AugmentedKrylovResult containing the solution and updated augmentation vectors.