Consider the Euclidean norm 1/2 n 3) = ||| i=1 computed using floating point arithmetic. (a)...

 

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Consider the Euclidean norm 1/2 n 3) = ||| i=1 computed using floating point arithmetic. (a) Explain how you would implement this sum to minimize roundoff error in the compu- tation. Give an example where the result is more accurate than the obvious implemen- tation. (b) Give an example where the obvious implementation can create an overflow and discuss how one could avoid this problem. Consider the Euclidean norm 1/2 n 3) = ||| i=1 computed using floating point arithmetic. (a) Explain how you would implement this sum to minimize roundoff error in the compu- tation. Give an example where the result is more accurate than the obvious implemen- tation. (b) Give an example where the obvious implementation can create an overflow and discuss how one could avoid this problem.