3. Let f(x) = (1+x)/3 - 1. We want to compute y = f(x) for x...

   

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3. Let f(x) = (1+x)¹/3 - 1. We want to compute y = f(x) for x = 10-4. (a) Compute y in Matlab in the straightforward way. Find the relative error using vpa. Which operation causes the large relative error? (b) Find a better algorithm which approximates y using a Taylor polynomial pn (x). Find the relative error using vpa. What value of n do you need? (c) Find a better algorithm using expm1, log1p. Find the relative error using vpa. Hint: First compute s such that 1 + x = e³. (d) Use expm1, log1p to compute y =√16-x-4 for x = 10-6. Find the relative error using vpa. 3. Let f(x) = (1+x)¹/3 - 1. We want to compute y = f(x) for x = 10-4. (a) Compute y in Matlab in the straightforward way. Find the relative error using vpa. Which operation causes the large relative error? (b) Find a better algorithm which approximates y using a Taylor polynomial pn (x). Find the relative error using vpa. What value of n do you need? (c) Find a better algorithm using expm1, log1p. Find the relative error using vpa. Hint: First compute s such that 1 + x = e³. (d) Use expm1, log1p to compute y =√16-x-4 for x = 10-6. Find the relative error using vpa.

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This question is about numerical computation of the function fx 1 x13 and finding ways to minimize the relative error in the calculations particularly when dealing with small values of x Lets go throu... View the full answer