Struct NeumannSolver 

pub struct NeumannSolver { /* private fields */ }

Neumann series solver implementation.

Solves systems of the form Ax = b by reformulating as (I - M)x = D^(-1)b where M = I - D^(-1)A and D is the diagonal of A.

The solution is computed using the Neumann series: x = (I - M)^(-1) D^(-1) b = Σ_{k=0}^∞ M^k D^(-1) b

For diagonally dominant matrices, ||M|| < 1, ensuring convergence.

Implementations

impl NeumannSolver

pub fn new(max_terms: usize, series_tolerance: Precision) -> Self

Create a new Neumann series solver.

Arguments

• max_terms - Maximum number of series terms (default: 50)
• series_tolerance - Tolerance for series truncation (default: 1e-8)

Example

use sublinear_solver::NeumannSolver;

let solver = NeumannSolver::new(16, 1e-8);

pub fn default() -> Self

Create a solver with default parameters.

pub fn high_precision() -> Self

Create a solver optimized for high precision.

pub fn fast() -> Self

Create a solver optimized for speed.

pub fn with_adaptive_truncation(self, enable: bool) -> Self

Configure adaptive truncation.

pub fn with_power_caching(self, enable: bool) -> Self

Configure matrix power caching.

Trait Implementations

impl Clone for NeumannSolver

fn clone(&self) -> NeumannSolver

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for NeumannSolver

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl SolverAlgorithm for NeumannSolver

fn solve( &self, matrix: &dyn Matrix, b: &[Precision], options: &SolverOptions, ) -> Result<SolverResult>

Custom solve implementation that provides matrix access to steps.

type State = NeumannState

Solver-specific state type

fn initialize( &self, matrix: &dyn Matrix, b: &[Precision], options: &SolverOptions, ) -> Result<Self::State>

Initialize the solver state for a given problem.

fn step(&self, state: &mut Self::State) -> Result<StepResult>

Perform a single iteration step.

fn is_converged(&self, state: &Self::State) -> bool

Check if the current state meets convergence criteria.

fn extract_solution(&self, state: &Self::State) -> Vec<Precision>

Extract the current solution from the state.

fn update_rhs( &self, state: &mut Self::State, delta_b: &[(usize, Precision)], ) -> Result<()>

Update the right-hand side for incremental solving.

fn algorithm_name(&self) -> &'static str

Get the algorithm name for identification.