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Unformatted text preview: Thermocline??? 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 yixi + = xi3a1 xi4a2 yixi2 • We denote Force ( ) Ff as y and velocity ( ) vf as x values, therefore we will get: Code used: >> x=10:10:80;...
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This note was uploaded on 12/20/2010 for the course E E 231 taught by Professor Vorobyov during the Spring '10 term at University of Alberta.
- Spring '10