Question #14048

(Demonstrating cancellation errors) A cancellation error
occurs when you are manipulating a very large number with a
very small number. The large number may cancel out the
smaller number. For example, the result of 100000000.0 +
0.000000001 is equal to 100000000.0. To avoid cancellation
errors and obtain more accurate results, carefully select
the order of computation. For example, in computing the
following series, you will obtain more accurate results by
computing from right to left rather than from left to
right:
1+1/2+1/3+...+1/n
Write a program that compares the results of the
summation of the preceding series, computing from left to
right and from right to left with n = 7000.

Expert's answer

#include <iostream>

using namespace std;

int main()

{

double leftToRight = 0, rightToLeft = 0;

int n = 7000;

cout

<< "SUM( 1 / i), i in (1 .. 7000)" << endl;

for(int i = 1, j

= n; i <= 7000; ++i, --j)

{

leftToRight += 1.0 / i;

rightToLeft += 1.0 / j;

}

cout << "Left to right: "

<< leftToRight << endl;

cout << "Right to left: "

<< rightToLeft << endl;

getchar();

return 0;

}

using namespace std;

int main()

{

double leftToRight = 0, rightToLeft = 0;

int n = 7000;

cout

<< "SUM( 1 / i), i in (1 .. 7000)" << endl;

for(int i = 1, j

= n; i <= 7000; ++i, --j)

{

leftToRight += 1.0 / i;

rightToLeft += 1.0 / j;

}

cout << "Left to right: "

<< leftToRight << endl;

cout << "Right to left: "

<< rightToLeft << endl;

getchar();

return 0;

}

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