InterpolationDate: 03/06/2003 at 16:26:08 From: Milt Subject: Interpolation I cannot remember the formula for interpolating between two numbers. For example: 1 26.4 2 x 4 24.2 Thank you for your help. Milt Date: 03/07/2003 at 11:08:41 From: Doctor Douglas Subject: Re: Interpolation Hi, Milt, You want a linear function that satisfies f(1) = 26.4, f(4) = 24.2, and we then want to compute f(2). You can start from the formula for a line: f(z) = mz + b, and solve for the constants m and b from the given data. That's one way to do it by brute force. There is also a way to write down the function by constructing it cleverly so that it goes through the data points when z takes on the appropriate values: f(z) = 26.4[(z-4)/(1-4)] + 24.2[(z-1)/(4-1)] Now this is clearly a linear function, and we've built up the square brackets from the given data such that when z=4, the first bracket disappears, the second bracket is equal to 1, and f(4) = 24.2. When z=1, the first bracket is equal to 1 and the second bracket disappears, so f(1) = 26.4. You can "simplify" this expression by multiplying out the constants and combining things, if you wish. And you can easily plug z=2 into this equation to find x = f(2). I hope this helps. Let me know if you'd like to talk about this some more, or if you have any other questions. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/ |
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