Numerical Error in program
To understand numerical errors in computers.
Error of input data
Input data error occurs when real number such as infinite decimal numbers are input as finite decimal number by users.
For example, square root are generated by approximate calculation such as iterative method and bisection method in computers.
Round-off error is caused because the calculation result is rounded to within the number of significant digits in computers.
1.105982 -> 1.10598
40156.245618 -> 40156.24562
Truncation error occurs when iterative calculation such as infinite series or iterative method aborted halfway because of time restriction.
Loss of significance
Loss of significance occurs in calculations of two close numbers using finite-precision arithmetic.
1.222222- 1.222221 = 0.000001
(significant digits 7) – (significant digits 7) = (significant digits 1)
Why loss of significance is undesirable?
For example, calculate √1000 – √999 to 7 significant digit.
Information loss occurs when add or subtract big number and small number.
122.2222 + 0.001234567 = 122.2234 (significant digits 7)