Re: a big limit of mathematica?
- From: "Dana" <delouis@xxxxxxxxxxxxx>
- Date: Sat, 10 Sep 2005 14:31:35 -0400
Hi. Thanks. I didn't even think about testing the equation exactly. You're
right, the Det quickly drops to zero from 3 onward.
I looked at a small table matrix, but I'm not that good to quickly spot the
reason the Det is zero.
equ=Simplify[(i-j)+3/j^4+50*i]
51*i+3/j^4-j
Table[Det[Table[equ,{i,n},{j,n}]],{n,1,10}]
{53, 3111/16, 0, 0, 0, 0, 0, 0, 0, 0}
$Version
"5.2 for Microsoft Windows (June 20, 2005)"
Here's another technique for posting those small numbers. This breaks the
number into the Mantissa, and Exponent.
MantissaExponent[Table[Det[Table[equ,{i,n},{j,n}]],{n,100,600,100}]]
{{0.,-307},
{-0.1105855292517657,-2290},
{ 0.7945106897056127,-3315},
{-0.2082885926840762,-4314},
{-0.4993937307336691,-5285},
{-0.1384814122285155,-6265}
}
--
Dana DeLouis
"Richard Fateman" <fateman@xxxxxxxxxxxxxxx> wrote in message
news:AODUe.5012$wk6.2867@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Dana wrote:
>> Hi. Looks like as the size of your matrix gets bigger, the Determinant
>> tends towards zero.
>> However, I can't explain why with a size 100*100 (the first output), it
>> returns "0." and with the largest sizes, numbers that are very small.
>>
>> In[1]:=
>> Simplify[(i-j)+3/j^4+50*i]
>>
>> Out[1]=
>> 51*i+3/j^4-j
>>
>> In[2]:=
>> Table[Det[Table[51.*i+3/j^4-j,{i,n},{j,n}]],{n,100,400,100}]
>>
>>
>> Out[2]=
>> {0.,
>> -1.1058552925176574276594077*^-2291,
>> 7.9451068970561274753784538*^-3316,
>> -2.0828859268407618803830820*^-4315
>> }
>>
>>
>>
>>
> In Mathematica 5.0.0 on an Intel Pentium 4,
>
> {
> -2.3072190778544011494885203792388`15.954589770191005\
> *^-1432,
> 1.6138130601828444080943999966955787`15.9545897701910\
> 05*^-2817,
> -2.17670639763548416057774043151`15.954589770191005*^\
> -4180,
> 1.283924316663441664176128821`15.954589770191005*^-55\
> 02}
>
> So the result "0.0" is a recent innovation. On my
> system, the Precision of the first number is 15.9546
> (decimal digits), not MachinePrecision, which makes
> one wonder what is going to happen in version 5.3 or 5.4.
> Mathematica's numerical model has been criticized by
> several people (including me), since Mathematica 1.0.
>
>
> If you do the calculation EXACTLY by using 51 instead of "51."
> the determinant of the 100X100 matrix comes out exactly 0.
> In fact, the determinant of the 10x10, 20x20 etc all come out
> exactly 0.
>
> The advantage of doing exact arithmetic (and using a CAS
> like Mathematica, Maple,Macsyma etc) over Matlab, is that the results
> can often be exactly right. In Matlab the result will
> be exactly right only by coincidence.
>
> For example, is there anything special about 51.0, 51.000000000000000 or
> exactly 51? Well, why not just put in a symbol, like A instead
> of 51. and compute the determinant. the 10X10 determinant
> is exactly zero. I assume that knowing the answer you can prove
> the determinant is zero always.
>
> Try that in Matlab. Actually, matlab can be coerced to doing
> it, but only by calling Maple. A much more versatile system
> then would actually be sometime like Mathematica, which could,
> if necessary for efficiency, call Matlab. The Mathematica
> people claim to be doing that, or maybe they claim to have
> already done that.
>
> So, for the original poster: your complaint about mathematica
> running out of memory has not been solved, but your reason for
> trying that computation is probably no longer compelling.
>
> RJF
>
>
.
- References:
- a big limit of mathematica?
- From: LumisROB
- Re: a big limit of mathematica?
- From: Dana
- Re: a big limit of mathematica?
- From: Richard Fateman
- a big limit of mathematica?
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