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Unformatted text preview: Data fitting and interpolation Curve Fitting Topics: Fitting data to a linear equation (method) Assessing goodnessoffit (coef. of determination) Fitting data to polynomial equations using MATLAB builtin functions polyfit, polyval (Sec 8.2.1) Using MATLAB data fitting tools 2/17/2009 1 Fitting data to an exponential equation (Sec 8.2.2) MASE201 Spring 2009 Fitting data to an equation Curve fitting is an activity in almost every lab: Usually, experimental data is gathered and the data is fit to an expected theoretical equation with one or more coefficients Usually there are multiple discrete data points to fit and the system is overdetermined (i.e. more data points than oefficients to fit) 2/17/2009 2 coefficients to fit) The data may have measurement errors or uncertainty MASE201 Spring 2009 Error Minimization Since we do not expect to find a solution where the predicted results using the equation are identical to the measured results at every data point then the problem becomes: Find the parameters in the theorertical equation that minimize the error between the experimental data 2/17/2009 3 and the theoretical result What do we define as error ? Should increase if the difference between the predicted result and experimental result increases Should include the contribution of all data points How do we find the minimum of the error once we have defined what error is? MASE201 Spring 2009 Fitting data to a linear equation Given n pairs of experimental data ( x i , y i ) Fit data to a theoretical equation of the form: If n = 2 , then we have 2 equations and 2 unknowns nd we can find a unique o a x a x f + = 1 ) ( + = = + = = 2 1 2 2 1 1 1 1 1 ) ( ; ) ( y a x a x a x f y a x a x f y o o 2/17/2009 4 and we can find a unique solution for [ a o , a 1 ] If n > 2 , then there are more data pairs than equations...
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