On 3/16/10 12:38 AM, Robert Dodier wrote:
> On 3/15/10, Luigi Marino <luigi_marino2 at alice.it> wrote:
>
>
>> Can Maxima integrate numerical
>> the function x^x^x from 1 to 6 or from 5 to 6 ?
>> It is a problem of the ISSAC'97 Systems Challenge.
>>
> You can try the bromberg (bigfloat romberg) function.
> load(brmbrg) loads it. It is undocumented, sorry, but it
> works like romberg.
>
> Just playing around a little, I get a result for
> bromberg(x^x^x,x,5,5.01) => 4.834235552810633b2240
> (no idea how accurate that is) but it fails with
> "too many iterations" or something like that for
> bromberg(x^x^x,x,5,5.1). Maybe you can increase
> brombergit (maxima number of iterations).
>
Since the integrand grows so fast, it makes sense to look at only the
integrand near 6. In fact at 5.999b0, the integrand is 2b36200. Hence
the integral from 1 to 5.999b0 is certainly less than 6 *2b36200.
bromberg(x^x^x, 5.999b0, 6b0) returns 1.102665003313474b36300, which is
1b100 times bigger than 12b36200, so I would say the value of the
integral is 1.1b36300.
Ray