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You are not logged in. #1 20110129 07:23:55
Thiele's Interpolation Formula  Inverse PhenomenonHello! you get the formula which, on the domain from 0 to 100 creates a pretty graph whose derivatives are 9 when x = 0, 1 when x = 25, and 1/9 when x = 100, simply using the values of x from the points given above. What's bizarre is that the function has an inverse of itself across the vertical asymptotic line and in the second quadrant which is shifted over by a value equal but negative to the second x value (25)and up by the second y value (75). The inverse in the second quadrant therefore has derivatives equal to and equidistant to those of the function's curve in the first quadrant, proving they are the same. How does this work? How can a function contain its own inverse? My observation of this goings on stems from my attempts at curve fitting which can be found elsewhere in the "Help Me!" portion of the forum, though by now I believe it must be buried several pages back. Thank you for your input! #2 20110129 13:36:08
Re: Thiele's Interpolation Formula  Inverse PhenomenonHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20110129 16:32:46
Re: Thiele's Interpolation Formula  Inverse PhenomenonYep. You never got back to me. The question I have now is about deriving the formula and, hopefully, learning about the formula itself. I thought it more appropriate, therefore, in the formula forum. #4 20110129 16:49:52
Re: Thiele's Interpolation Formula  Inverse PhenomenonHi Reule; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #5 20110129 16:54:01
Re: Thiele's Interpolation Formula  Inverse PhenomenonNo, the derivatives would be the same. #6 20110129 17:01:48
Re: Thiele's Interpolation Formula  Inverse Phenomenon
Yes, in the fit, but a fit was impossible, I think because of the problem with the derivatives being different at the same x value for the two piecewise functions. That is why they could not be joined into one function. You were also asking for a interpolating fit ( exact ). For many discontinous functions that is not possible. Just explaining why there was no reply, I failed in the attempt even though I used thousands of points and 3 computers! Mathematically, I suspect the above reason will not allow the problem to be solved. That is how it is done. The p() are the reciprocal differences, very hard to compute by hand. This is clearly a job for a computer. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20110130 10:17:50
Re: Thiele's Interpolation Formula  Inverse PhenomenonAll respect, working in as many "last words" as possible and copying and pasting, so to speak, from Wikipedia isn't helping. I taught myself how to do the formula by hand a year ago when my math teacher refused to teach it to me. What I am looking for is a derivation of the formula. #8 20110130 10:24:57
Re: Thiele's Interpolation Formula  Inverse Phenomenon
That is a good idea because as I understand it Thiele and Fisher ( the statistician ) were coworkers. I have never seen the derivation of it. So I thank you beforehand.
Maybe he was right? From a Numerical Analyst point of view I am forced to agree. As a practical method it is a hopeless jumble and there are better ways. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20120321 19:17:07
Re: Thiele's Interpolation Formula  Inverse Phenomenonhi can i ask about how does the formula of linear interpolation derived from? #10 20120321 19:24:29
Re: Thiele's Interpolation Formula  Inverse Phenomenonhelp me please i cant understand how does it derived from the only fact i know is that it is connected to the two point slope form #11 20120321 19:25:10
Re: Thiele's Interpolation Formula  Inverse PhenomenonHi; The derivation is on the top of this page: http://en.wikipedia.org/wiki/Linear_interpolation It can be derived from what I call the point  point formula of Cartesian geometry. basically, if you want to linearly interpolate between two data points you fit a straight line between those two points and then just plug in. There is also a method that can do this interpolation. Welcome to the forum! In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 