Errors in Computations

This is the preliminary in Basic Numerical Methods.

Computer and Errors

There are many types of error. In class, we discussed four.

Round-off error - errors made when rounding off numbers or truncating numbers.

 Example:

Given: 2.54674  
Computer rounding it off to the nearest hundreds: 2.55

Propagation - error usually occur in software programming, a normal error
                     - error within an error, what we call the butterfly effect

Example:    Given:  The machine can take in two numbers to the right of the decimal places.
                              $f(x)=x^2+7x, x=0.12$

Manual Solution:
$ f(0.12)=(0.12)^2+7(0.12)=0.0144+0.84=0.8544$
Machine's Solution:
$f(0.12)=(0.12)^2+7(0.12)=0.014+0.84=0.85$

Underflow and Overflow - too much error in the exponents, if the number is too small or to big.