- #1

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why we do tailor around 1 and not 0

?

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- Thread starter nhrock3
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- #1

- 415

- 0

why we do tailor around 1 and not 0

?

Last edited:

- #2

tiny-tim

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You can "Taylor" around

But it

(and I expect they've chosen z = 1 because it's easiest to calculate the derivatives there! )

- #3

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so when x=y we have a problem

how transforming it into a taylor series solves this accuracy problem?

how transforming it into a taylor series solves this accuracy problem?

- #4

Mark44

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Why do you think there is a problem when x = y? If x = y, log(x/y) = log(1) = 0.

- #5

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f=ln x -ln y

x,y>0

and the solution says that we have a problem when x and y are close to each other

how transforming it into a taylor series solves this accuracy problem?

- #6

Mark44

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By using a Taylor series to approximate log(x) - log(y) = log(z) [itex]\approx[/itex] z - 1, the part after the zeros above is now significant.

- #7

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"limitations in computing precision"

how does this limitation get solves by this method?

- #8

Mark44

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So if you have two numbers that are very different in relative size, (e.g. 1 vs. .00000000000125), adding them causes the loss of digits. If you can strip off the 1, though, there's no problem in storing or computing with the part to the right of all the zeros. In computers, floating point numbers are stored in a way that is similar to scientific notation. Instead of being stored as .00000000000125, it would be stored something like 1.25 X 10

number like 1.00000000000125, where one part is very large

- #9

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f=ln x -ln y?

f=ln x -ln y=ln z

the tailor series for ln z is:

[tex] \sum_{k=1}^{\infty}\frac{(-1)^{k+1}(Z-1)}{k}[/tex]

but how this expression equals z-1 ?

- #10

Mark44

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