uni20::krylov::GmresErrorEstimates< R > Struct Template Reference

Error estimates evaluated from the residual and supplied operator data. More...

#include <gmres_diagnostics.hpp>

Public Attributes
std::optional< R >	absolute_solution_error = {}
	||A^{-1}|| ||r||, requiring an inverse norm.
std::optional< R >	normwise_backward_error = {}
	||r|| / (||A|| ||x_hat|| + ||b||), requiring an operator norm.
GmresOperatorEstimates< R >	operator_estimates = {}
std::optional< R >	relative_solution_error = {}
	kappa(A) ||r|| / ||b||, relative to the exact solution norm.

Detailed Description

template<Real R>
struct uni20::krylov::GmresErrorEstimates< R >

Error estimates evaluated from the residual and supplied operator data.

All outputs are estimates: even a known operator bound does not bound rounding error in the computed residual. An overflowing diagnostic is infinity and does not invalidate the solve. Missing information leaves a field absent. Supplied provenance is retained at diagnostic precision.

Member Data Documentation

absolute_solution_error

template<Real R>

std::optional<R> uni20::krylov::GmresErrorEstimates< R >::absolute_solution_error = {}

||A^{-1}|| ||r||, requiring an inverse norm.

normwise_backward_error

template<Real R>

std::optional<R> uni20::krylov::GmresErrorEstimates< R >::normwise_backward_error = {}

||r|| / (||A|| ||x_hat|| + ||b||), requiring an operator norm.

operator_estimates

template<Real R>

GmresOperatorEstimates<R> uni20::krylov::GmresErrorEstimates< R >::operator_estimates = {}

relative_solution_error

template<Real R>

std::optional<R> uni20::krylov::GmresErrorEstimates< R >::relative_solution_error = {}

kappa(A) ||r|| / ||b||, relative to the exact solution norm.

Requires a condition number or both norms; absent for zero RHS. An explicitly supplied condition number takes precedence.

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The documentation for this struct was generated from the following file:

• gmres_diagnostics.hpp