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Unformatted text preview: 240 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES Determine the model parameters in each case using least square estimation method using the following data: Formulate the problem as minimization of || e || 2 = || Ac Y || 2 and f nd the projection matrix P r that projects vector Y onto the column space of A. Find the model prediction vector Y = Ac and the error vector e = Y Y using the projection matrix. Assuming that the errors are normally distributed, estimate the covariance matrix of the estimated parameters and correlation co- e cient in each case and compare the two models. c p ( KJ/kgK ) T ( K ) c p ( KJ/kgK ) T ( K ) 1.426 150 1.627 230 1.469 170 1.661 240 1.516 190 1.696 250 1.567 210 1.732 260 (11) Very common model for a dimensionless f rst-order chemical reaction is dC/dt = kC with C (0) = 1 . The integrated form of this model is C = exp ( kt ) , which is non linear in the parameter k. Solve this problem by f rst transforming the model to linear form to...
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