Re: A new proof of the superiority of set oriented approaches: numerical/time serie linear interpolation
From: Gene Wirchenko <genew_at_ocis.net>
Date: Thu, 03 May 2007 12:13:02 -0700
Message-ID: <3vck3390h8c48k6kdgoap2k96uh8prbdlt_at_4ax.com>
>
>I don't recall claiming that f(x) was a function. I recall claiming it
>was a trap for interpolation.
Date: Thu, 03 May 2007 12:13:02 -0700
Message-ID: <3vck3390h8c48k6kdgoap2k96uh8prbdlt_at_4ax.com>
Bob Badour <bbadour_at_pei.sympatico.ca> wrote:
>Gene Wirchenko wrote:
>
>> Bob Badour <bbadour_at_pei.sympatico.ca> wrote:
>>
>>
>>>Gene Wirchenko wrote:
>>>
>>>
>>>>Bob Badour <bbadour_at_pei.sympatico.ca> wrote:
>>>>
>>>>[snip]
>>
>>
>>>>>Interpolation has a number of other traps. Suppose one evaluates:
>>>>>f(x) = (x-1)/(x-1) at x=0 and x=2. One will reach a vastly wrong
>>>>>conclusion if one even tries to interpolate f(1).
>>>>
>>>> What about if we limit it to functions? Your f is not a
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>>>>function, because 1 is not in the domain. (I am assuming a general
>>>>(for lack of a better word) domain, such as N, Z, Q, or R.)
>>>
>>>If 1 were not in the domain, one would have no desire to interpolate to
>>>it in the first place. That sounds like ignoring the problem by defining
>>>it out of existence.
>>
>> If 1 is in the domain, then f(x) does not have a defined value
>> for 1, and is, thus, not a function.
>
>I don't recall claiming that f(x) was a function. I recall claiming it
>was a trap for interpolation.
- What about my question above?
- How about f(x)=sqrt(x)? For x>0, it has two answers. Try interpolating on that.
Sincerely,
Gene Wirchenko
Computerese Irregular Verb Conjugation:
I have preferences.
You have biases.
He/She has prejudices.
Received on Thu May 03 2007 - 21:13:02 CEST