Matrix computations &
Numerical linear algebra

David Gleich

Purdue University

Fall 2012

Course number CS-51500

Tuesday and Thursday, 10:30-11:45am

Location Lawson 1106

Quiz 16

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Let $\vr = \vb - \mA \vx$ be the residual for an approximate solution $\vx$. Let $\mA \vy = \vr$. Show that $\normof{\vy} = \normof{\mA^{-1} \vb - \vx}.$

Solution $\mA \vy = \vr = \vb - \mA \vx$ implies that $\vy = \mA^{-1} \vb - \vx$. Now we just take norms.