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Re: while loop - numerics

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Am 18.05.2011 13:17, schrieb Anna Kaladze:
> Hi all,
>
>
>
> I am new in loop writing in Mathematica, so your help on the following
> seemingly simple problem would be appreciated.  I have the following
> commands:
>
> -------------------------------------------------
>
> tol=1/100;
>
>
>
> DM=9;
>
>
>
> yguess=0.5;
>
>
>
> x=yguess^2
>
> 0.25
>
>
>
> yfeedback=x*yguess
>
> 0.125
>
>
>
> Error=Abs[yfeedback-yguess]
>
> 0.375
> -------------------------------------------
> Without doing any equations solving/substitutions or any algebraic
> manipulations, or utilizing Table commands, I need to have a while loop
> command applied to the above code, such that for a given yguess value
> entered (now it is set to 0.5 for the first iteration), Mathematica would
> calculate yfeedback and the Error, every time updating yguess with the
> following rule: yguess = the last calculated value of yguess*(1+last
> calculated value of Error/DM), until Error in the last iteration is less or
> equal tol. And then report what that yguess value is.
>
> For yguess = 0.5, we obviously get after 1st iteration that yfeedback=0.125
> and a large resulting Error value 0.375. So, the yguess needs to be updated
> as 0.5*(1+0.375/DM), and that would become 0.520833. Now in the second
> iteration yguess takes the value of 0.520833, and then the resulting Error
> would become 0.379548, and then the updated yguess would become
> 0.520833*(1+0.379548/DM)= 0.542798 and so on until the stopping criteria is
> achieved. (Somewhere when the program calculates yguess close to unity the
> program should stop obviously). The question is how to write such a code.
>
> Thanks in advance.
>
> Anna

Hi Anna,

this is a typical problem for "NestWhile[..]". The following function 
will return the pair {yguess, error} when the termination condition is 
satisfied. I built it with two emergency brakes; one restricts the 
number of iterations to 10000 and the other breaks when the error 
becomes greater than 10^10 (iteration diverges):

iterate[yguess_]:=
   Block[{tol = 1/100, DM = 9, tmp},
     NestWhile[{tmp = #[[1]](1 + #[[2]]/DM), Abs[tmp(tmp^2 - 1)]} &,
       {yguess, Abs[yguess(yguess^2 - 1)]},
      10^10 > #[[2]] > tol &,1,10000]
   ]

if you use "NestWhileList" in place of "NestWhile", you'll get a list of 
all calculated {guess, error} - pairs.

hth,
Peter

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while loop - numerics Anna Kaladze <anna.kaladze@gmail.com> - 2011-05-18 11:17 +0000
  Re: while loop - numerics Peter Pein <petsie@dordos.net> - 2011-05-19 11:43 +0000

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