ee231_HW9 - EE 231_B1 Numerical Analysis for Electrical and...

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EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov Damir Iraliyev, 1246540 Assignment 9 14.2 Using the same approach as was employed to derive Eqs.(13.15) and (13.16), derive the least squares fit of the following model: = + + y a1x a2x2 e That is, determine the coefficients that result in the least-squares fit for a second-order polynomial with a zero intercept. Test the approach by using it to fit the data from table 13.1. Table 13.1: Experimental data for force (N) and velocity (m/s) from a wind tunnel experiment. / vf m s 10 20 30 40 50 60 70 80 Ff N 25 70 380 550 610 1220 830 1450 Solution: For this case the sum of the squares of the residuals is: = = - - Sr i 07yi a1xi a2xi22 To generate the least-squares fit, we take the derivative of given equation with respect to each unknown coefficients of the polynomial, as in: =- - - Sr a1 2xiyi a1xi a2xi2 =- - - Sr a2 2xi2yi a1xi a2xi2 The above equations can be set equal to zero and rearranged to develop the following set of normal equations: + = xi2a1 xi3a2
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