Compute the quantities

with and and then with
and . Use both the above formula and an equivalent formula that avoids numerical cancellation. Let be the quantity computed with this second algorithm. Evaluate the relative errors for both the assigned pairs of data. Which of the following statement is correct?

Question

Compute the quantities 
  
 with    and    and then with
   and   . Use both the above formula and an equivalent formula that avoids numerical cancellation. Let    be the quantity computed with this second algorithm. Evaluate the relative errors    for both the assigned pairs of data. Which of the following statement is correct?

Accepted Answer

The relative errors are about 1.1e-07 and 5.6e-09 respectively, thus the numerical cancellation is more evident in the first case.

Answer

The relative errors are about 
1.1e-07 and 5.6e-09 respectively, thus the numerical cancellation is 
more evident in the second case.

Answer

The relative errors are about 6.1e-12 and 5.4e-07 respectively, thus the numerical cancellation is 
more evident in the second case.

Answer

The relative errors are about 6.1e-12 and 5.4e-07 respectively, thus the numerical cancellation is 
more evident in the first case.

Answer

None of the alternatives

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Compute the quantities with and and then with and . Use both the...

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