Re: [WWdevel] parser fun_cmp() error?

[Arnold P. <ap...@ma...>]

At 10:05 PM 9/22/2005, Davide P. Cervone wrote:

Hi Gavin,

You can also adjust the tolerances.  The default relTol is .1 meaning 
0.1%.  This may not be suitable for this problem.

Arnie


>>The following has come up in our on-line homework: I have a problem
>>the answer to which is a linear combination of exponentials (e^{- 
>>kt} with k small).  I'm using the Parser-based fun_cmp()
>>evaluator.  The correct answer is marked correct, but an incorrect
>>answer is also.
>>
>>The correct answer is
>>   (-201/94)*e^(-t/107) + (295/94)*e^(-t/201)
>>but the answer
>>   -e^(t(-1/107 -1/a))+2e^(-t/a)
>>with a (at least) between 175 and 250 also works.  If a is 300 it
>>doesn't work, however.
>>
>>Is this an accuracy issue?
>
>Yes and no.  Part of this will depend on the limits you are using for
>t, which you haven't given us.  So I'll assume you are using the
>default 0 to 1 range for t.  The two functions you site are nearly
>identical on that range, so they are being marked as the same,
>because they differ by such a small amount (less that .00005 for
>a=200, which is well below the tolerances).
>
>In fact, the functions are nearly linear (and nearly flat).  The
>constant value 1 is almost good enough to be marked as correct.  But
>the line 1+.004t IS good enough to be marked as correct.
>
>The original function is so flat for t > 0, you really need to go to
>a different range of t's if you want to distinguish this from other
>functions.  It looks to me like t's between -200 and -100 might be
>better for your purposes.  (Graph the functions and see.)
>
>Davide
>
>
>
>-------------------------------------------------------
>SF.Net email is sponsored by:
>Tame your development challenges with Apache's Geronimo App Server. 
>Download it for free - -and be entered to win a 42" plasma tv or your very
>own Sony(tm)PSP.  Click here to play: http://sourceforge.net/geronimo.php
>_______________________________________________
>OpenWeBWorK-Devel mailing list
>Ope...@li...
>https://lists.sourceforge.net/lists/listinfo/openwebwork-devel

Prof. Arnold K. Pizer
Dept. of Mathematics
University of Rochester
Rochester, NY 14627
(585) 275-7767