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Unformatted text preview: Data fitting and interpolation • Curve Fitting Topics: – Fitting data to a linear equation (method) – Assessing “goodness-of-fit” (coef. of determination) – Fitting data to polynomial equations using MATLAB built-in 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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- Spring '10
- Regression Analysis, Quadratic equation, Elementary algebra, Yi