Thread: numerical analisys close numbers question..

how do we know that there is a subtraction of two close numbers thus making loss of significance?
there is no close numbers there is variable X
it could give use a close result or otherwise

and why multiplying and dividing by
makes it go away?

Originally Posted by transgalactic

how do we know that there is a subtraction of two close numbers thus making loss of significance?
there is no close numbers there is variable X
it could give use a close result or otherwise

and why multiplying and dividing by
makes it go away?

I presume this means for x close to 0. For example, if x= 0.001, . If you are rounding to, say, 6 decimal places, That would be just 0. As for multiplying and dividing by the result, of course, will be the same but I presume that this is talking about it being some intermediate result in a further calculation- where the " " you would get in the numerator will be canceled.

we get x^2 in the nominator
and a sum in the denominator
now there is some stuff about relative error
but i dont know what?

Originally Posted by transgalactic

how do we know that there is a subtraction of two close numbers thus making loss of significance?
there is no close numbers there is variable X
it could give use a close result or otherwise

and why multiplying and dividing by
makes it go away?

I think you have already figured out that


The point of the exercise is that in this form the value can be computed without the catastrophic loss of significant figures that occurs in the original computation when x is small due to the subtraction of two almost-equal numbers.

Or, to put it another way, No Subtraction!