Matrix.BackError Property

Matrix Class

Double BackError { get; set; }

The component-wise backward error.

Returns: Double

Remarks:

Set by the Dew.Math.Matrix.LUSolve method, if the Dew.Math.Matrix.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:

∣δai,j∣∣ai,j∣≤βai,j∣δbj∣∣bj∣≤βbjsuch that(A+δA)x=b+δb\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 Dew.Math.Matrix.RefineSolution property is set to true.

See Also: Matrix.ForwError, Matrix.RefineSolution, Matrix.LUSolve