TMtx::BackError Property

__declspec(property(get = GetBackError)) double BackError;

The component-wise backward error.

Read: double GetBackError();

Remarks:

Set by the TMtx::LUSolve method, if the TMtx::RefineSolution property was True. The BackError property returns the component-wise backward error b. The backward error is the smallest relative perturbation in elements of A (where A is the calling matrix) and b such that x is the exact solution of the perturbed system:

\frac{|\delta a_{i,j}|}{|a_{i,j}|}\leq \beta a_{i,j} \quad \frac{|\delta b_{j}|}{|b_{j}|}\leq \beta b_{j} \quad \text{such that}\quad (A+\delta A)x=b+\delta b

The BackError property is calculated only if the TMtx::RefineSolution property is set to true.

See Also: TMtx::ForwError, TMtx::RefineSolution, TMtx::LUSolve

Declared in Dew::Math::TMtx · Dew.Math/MtxVec.h · Cross-compiler