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CSIR UGC NET PG 2020 : Physics : curvefitting

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CGN 3421 - Computer Methods Gurley Numerical Methods Lecture 5 - Curve Fitting Techniques Topics motivation interpolation linear regression higher order polynomial form exponential form Curve fitting - motivation For root finding, we used a given function to identify where it crossed zero where does ! ( " ) " ! ?? Q: Where does this given function ! ( " ) come from in the first place? Analytical models of phenomena (e.g. equations from physics) Create an equation from observed data 1) Interpolation (connect the data-dots) If data is reliable, we can plot it and connect the dots This is piece-wise, linear interpolation This has limited use as a general function ! ( " ) Since its really a group of small ! ( " ) s, connecting one point to the next it doesn t work very well for data that has built in random error (scatter) 2) Curve fitting - capturing the trend in the data by assigning a single function across the entire range. The example below uses a straight line function f(x) = ax + b for each line f(x) = ax + b for entire range Curve Fitting Interpolation A straight line is described generically by f(x) = ax + b The goal is to identify the coefficients a and b such that f(x) fits the data well Numerical Methods Lecture 5 - Curve Fitting Techniques page 89 of 102

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