Noisy Data Known to Estimate a Function
Date: 05/15/2003 at 20:56:37 From: Kharem Espinoza Subject: Finding the maximum value of a function with noise How do we find the maximum value of a function with a high level of noise?
Date: 05/16/2003 at 18:51:46 From: Doctor Douglas Subject: Re: Finding the maximum value of a function with noise Hi Kharem, Thanks for writing to the Math Forum. Do you mean that you have a set of data (which are noisy) that are known to estimate some function and you are trying to find the maximum of the function? I say that the data are "known to estimate a function" so that you might not want to simply take the maximum of the data set, which may be affected by the noise. Here are some ways you could proceed: 1. you could just take the maximum of the data and live with the noise. 2. you could "fit" the data in order to obtain a mathematical function (that might be differentiable, or otherwise easy to extract the maximum), given what you know about the function that describes the data. 3. you could interpolate the data with a polynomial, choosing the lowest order consistent with the number of points. Then you could find the maximum from the polynomial. I hope this helps you get started. There are some delicate issues that arise in fitting and interpolation, and these are compounded by the problem of noise. - Doctor Douglas, The Math Forum http://mathforum.org/dr.math/
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