= = XiYj. 4. (4 points) The outer product of x and y = R^ is...

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= = XiYj. 4. (4 points) The outer product of x and y = R^ is the matrix A - xy with entries Aj Suppose = fl(xy) and derive the componentwise forward error estimate | A| |A|u, where u is the unit roundoff. Why is it unlikely that has the form (x + Ax) (y + Ay)T? (As a result, computing outer products is not backward stable.) = = XiYj. 4. (4 points) The outer product of x and y = R^ is the matrix A - xy with entries Aj Suppose = fl(xy) and derive the componentwise forward error estimate | A| |A|u, where u is the unit roundoff. Why is it unlikely that has the form (x + Ax) (y + Ay)T? (As a result, computing outer products is not backward stable.)

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