does any body know how to write an iteration to compute y in y-log(y)=x ?

thank's,

dan

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- Jul 10th 2006, 08:28 AM #1

- Jul 10th 2006, 09:08 AM #2

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- Jul 10th 2006, 10:09 AM #3

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(I assume your question is on Newton's Method cuz that is what you asked the other time).

You want to solve,

Which is equivalent to,

The iteration sequence is,

Where,

Thus,

Thus,

Thus,

Simplfy,

More simplfying,

And yet one more time, (watch those signs )

Finally we have,

- Jul 10th 2006, 11:00 AM #4

- Jul 10th 2006, 11:14 AM #5

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- Jul 10th 2006, 01:47 PM #6

- Jul 10th 2006, 02:02 PM #7

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- Jul 10th 2006, 02:12 PM #8

- Jul 10th 2006, 02:30 PM #9

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Originally Posted by**dan**

iteration as given by PH it appears to diverge with , or !

It must be a mistake in PH's algebra as the iteration (which is what PH had before he tried simplifying it):

does converge with , to after two iterations.

RonL

- Jul 10th 2006, 03:15 PM #10

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- Jul 10th 2006, 03:33 PM #11

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- Jul 10th 2006, 07:09 PM #12Originally Posted by
**dan**

You are given x

Guess any value of a(a is iterating variable, should be greater than x)

Find

You will get some value

this is your next value of a

Substitute it again in the above expression.

After some steps it will give the answer(when you the same value of a for two times)

Note: I am not sure about this idea, please someone check it.

Keep Smiling

Malay

- Jul 10th 2006, 08:36 PM #13

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- Jul 11th 2006, 05:22 AM #14

- Jul 11th 2006, 05:39 AM #15

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