Error and residue in linear system

Question

Consider the linear system $A x = b$ with a computed solution, what will be the relation between error and residue?

How do you define error and residue? – mvw Apr 28 '16 at 10:55 — mvw, Apr 28 '16 at 10:55

score 0 · Answer 1 · answered Apr 28 '16 at 18:25

It will be helpful if you saw what you understand by error and residue.

In most literature, the residual corresponds to the vector of differences like: $\mathbf{r} = A\mathbf{x}-\mathbf{b}$. The error (usually an scalar quantity) corresponds to the norm of the residual: $e = ||A\mathbf{x}-\mathbf{b} ||$.

Error and residue in linear system

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