Question

Program of find the truncation error in a series of approximation in numerical computing using c++ languages

Answer 1

Answer:

The value of Exponential Function e^x can be expressed using following Taylor Series.

e^x = 1 + x/1! + x^2/2! + x^3/3! + ......

How to efficiently calculate the sum of above series?

The series can be re-written as

e^x = 1 + (x/1) (1 + (x/2) (1 + (x/3) (........) ) )

Let the sum needs to be calculated for n terms, we can calculate sum using following loop.

for (i = n - 1, sum = 1; i > 0; --i )

sum = 1 + x * sum / i;

Answer 2

Explanation:

Truncation error is the difference between a truncated value and the actual value.As an example of truncation error, consider the speed of light in a vacuum. The official value is 299,792,458 meters per second. In scientific (power-of-10) notation, that quantity is expressed as 2.99792458 x 108.