User talk:Ramiamro
numerical stability could be affected by the number of the significant digits the machine keeps on, for example , if we use a machine that keeps on the first five floating-point digits, a floating point number of the following form
- z=0.123456789114598765
assuming no round off , the number will be shown as
- z1 =0.12345
so the error will be
- z-z1=0.000006789114598765
and if we try to make a mathematical operation; for example take the square of z1
- z1.z1=0.015239902
the machine will show only the first five floaing-point digits which is
- 0.01523
with an error of about
- 0.065%
which is actually cosidered as a huge amount of error in one mathematical operation,if you imagine thousands of operations this error will grow up along the calculations, and so affect the stability of the algorithm. this phenomena is called loss of significance
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