Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Re: NIntegrate and Sequence

• To: mathgroup at smc.vnet.net
• Subject: [mg63578] Re: NIntegrate and Sequence
• From: "Kevin J. McCann" <kjm at KevinMcCann.com>
• Date: Fri, 6 Jan 2006 05:24:21 -0500 (EST)
• References: <200601021049.FAA01309@smc.vnet.net> <43B94E48.8050009@umbc.edu> <dpd6uo$q8t$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Note that the -1447 is multiplied by the 10th derivative. It is not 
clear that this error is "large". You make a speed/accuracy tradeoff by 
choosing different numbers of points. The choice means that you have to 
have some feeling for the problem. Note that 10^-14 times the 40th 
derivative (your last example) may be huge for noisy data even if the 
magnitudes of the points themselves are small.

Kevin


Pratik Desai wrote:
> Pratik Desai wrote:
> 
> 
>>Bob Hanlon wrote:
>>
>>
>>>Nintegrate has the attribute HoldAll.
>>>
>>>Attributes[NIntegrate]
>>>
>>>{HoldAll,Protected}
>>>
>>>Use Evaluate.
>>>
>>>NIntegrate[r,Evaluate[{r,14,Sequence@@{16,18},40}]]
>>>
>>>702.
>>>
>>>
>>>Bob Hanlon
>>>
>>> 
>>>
>>>
>>>>From: Bruce Colletti <vze269bv at verizon.net>
To: mathgroup at smc.vnet.net
>>>>Date: 2006/01/01 Sun AM 01:16:12 EST
>>>>Subject: [mg63578]  NIntegrate and Sequence
>>>>
>>>>Re Mathematica 5.2 under WinXP.
>>>>
>>>>The first command works while the other returns the NIntegrate::nlim 
>>>>error.    
>>>
>>>Yet {r, 14, Sequence @@ {16, 18}, 40} returns {r,14,16,18,40}.   
>>>
>>>
>>>>NIntegrate[r, {r, 14, 16, 18, 40}]
>>>>NIntegrate[r, {r, 14, Sequence @@ {16, 18}, 40}]
>>>>
>>>>What is causing the error?
>>>>
>>>>Thankx.
>>>>
>>>>Bruce
>>>>
>>>>  
>>>
>>I tried using GaussianQuadrature, why is the error so high for this 
>>interval (see out 49)
>>
>>
>>In[46]:=
>><<NumericalMath`GaussianQuadrature`
>>data1=GaussianQuadratureWeights[5,14,40]
>>ans=Table[Times@@data1[[r]],{r,1,Length[data1],1}]//Total
>>GaussianQuadratureError[5,f,14,40]//InputForm
>>
>>Out[47]=
>>{{15.2197,3.08005},{19.9999,6.22217},{
>> 27.,7.39556},{34.0001,6.22217},{38.7803,3.08005}}
>>
>>Out[48]=
>>702.
>>
>>Out[49]//InputForm=
>>-1447.938207040937*Derivative[10][f]
>>
>>
>>
>>
> 
> I found the problem, had to increase the number of Gauss points
> GaussianQuadratureError[20, f, 14, 40] // InputForm
>  >>-1.6243254536030502*^-14*Derivative[40][f]
> 
> 
> 

• References:
  • Re: NIntegrate and Sequence
    • From: Bob Hanlon <hanlonr@cox.net>