Stanford UniversityMATH 104math104hw6

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Problem Set 6 Solutions Problem 1: (a) We will show that f(x) = 2x computed via the algorithim f~(x) = x ⊕ x is backwards stable (and hence also stable). Our computations in this problems are all with real numbers, so we may take the norm to be absolute value. We need to show there exists ~ x with jx − x~j jxj = O(machine) that statisfies f~(x) = f(~ x). Our control over the problem comes from choosing ~ x, so we start by computing f~(x) and figuring out what ~ x must be. Note that...

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