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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