Transcription of ECE 1010 ECE Problem Solving I Interpolation and 6 Curve ...
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ECE 1010 ECE Problem Solving I Interpolation and 6 Curve ...
ECE 1010 ECE Problem Solving IChapter 6: Overview6 1 Interpolation and Curve FittingOverviewGiven a set of data that results from an experiment (simulationbased or otherwise), or perhaps taken from a real-life physicalscenario, we assume there is some function that passesthrough the data points and perfectly represents the quantity ofinterest at all non- data points. With Interpolation we seek a func-tion that allows us to approximate such that functional val-ues between the original data set values may be determined(estimated). The interpolating function typically passes throughthe original data set. With Curve fitting we simply want a func-tion that is a good fit (typically a best fit in some sense) to theoriginal data points. With Curve fitting the approximating func-tion does not have to pass through the original data set. An example of Interpolation using spline functions and least-squares Curve fitting using a fifth degree polynomial is shownin the following figure The data set is a set of 10 random numbers generated using10*rand(1,10) Note that the spline Interpolation passes through the datapoints while the Curve fit does notfx()fx()6 ECE 1010 ECE Problem Solving IChapter 6: Interpolation6 2 A higher degree polynomial would presumably give a bet-ter fitInterpolation The simplest type of int
ECE 1010 ECE Problem Solving I Chapter 6: Overview 6–1 Interpolation and Curve Fitting Overview Given a set of data that results from an experiment (simulation
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