= 5. Consider the problem y h(x1, x) = x1x2 of multiplying two nonzero real numbers....

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= 5. Consider the problem y h(x1, x₂) = x1x2 of multiplying two nonzero real numbers. On a computer the algorithm for approximating the product is yA = hA(x1, x2) = f(x1) fl(x2), where is the inexact floating point multiplication. Show that the algorithm is backwards stable. That is, show hA(x1, x2) = h(x1 + 8x1, x2 + 8x2), where 8x1/x1 = O(Emach) and 6x2/x2] = 0(Emach). Is the perturbation of the inputs unique? = 5. Consider the problem y h(x1, x₂) = x1x2 of multiplying two nonzero real numbers. On a computer the algorithm for approximating the product is yA = hA(x1, x2) = f(x1) fl(x2), where is the inexact floating point multiplication. Show that the algorithm is backwards stable. That is, show hA(x1, x2) = h(x1 + 8x1, x2 + 8x2), where 8x1/x1 = O(Emach) and 6x2/x2] = 0(Emach). Is the perturbation of the inputs unique?

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Problem Statement Function y hx1 x2 x1 x2 multiplying two nonzero real numbers Approximation Algorithm yA hx1 x2 x1x2 using inexact floatingpoint multiplication Task Demonstrate backward stability of ... View the full answer