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Unformatted text preview: f nonzero and the other components zero). Any other change gives a bigger E F . Thus the smallest value of the minimization function is n +1 , and since we veriFed in part (a) that our solution has this value, we are Fnished. If you dont Fnd that argument convincing, we can be more precise. We use a fact found in the Frst pointer in Chapter 2: for any matrix B and vector z for which Bz is deFned: Bz 2 B 2 z 2 , where B 2 is deFned to be the largest singular value of B . Therefore, B 2 B F , since we can see from part (b) and the singular value decom-position of B that the robenius norm of B is just the square root of the sum of the squares of its singular values. If ( + E ) f = , then f = E f ....
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- Fall '11