Chemical Engineering Hand Written_Notes_Part_87

Chemical Engineering Hand Written_Notes_Part_87 - 176 5...

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176 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES These assumption considerably simpli f es problem formulation. Under these assumptions, the model parameter estimation problem can be stated as estima- tion of θ such that min θ f ( e 1 ,e 2 , ..... e N ) e i = y i b y £ x ( i ) , θ ¤ ; i =1 , 2 , .... N 3.4. Interpolation and Approximation. Problem de f nition : Let aset { x ( i ) : i =1 , ...N } of variable x corresponds to a set { y i : i =1 , ....... N } of variable y and let (3.16) b y = f ( x 1 , ..... θ m ) represent the proposed model where f is a continuous function linear in para- meters. Substituting x i we get (3.17) b y i = f ¡ x ( i ) 1 , ..... θ m ¢ ( i =1 , 2 ...... N ) a set of N linear equations in m unknowns. Case ( N = m ): If N equations are independent then a unique solution exists and we can obtain the function b y = f ( x 1 , ...θ m ) passing through each of these N points i.e. we have done an interpolation. Case
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This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

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Chemical Engineering Hand Written_Notes_Part_87 - 176 5...

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