Chemical Engineering Hand Written_Notes_Part_21

Chemical Engineering Hand Written_Notes_Part_21 - 44 2....

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44 2. FUNDAMENTALS OF FUNCTIONAL ANALYSIS Inverse Problems: Given operator F and y , f nd x . In this case we are looking for input which generates observed output. Solving system of simultaneous (linear / nonlinear) algebraic equations, ordinary and partial di f erential equations and integral equations are examples of this category Identi f cation problems: Given operator x and y , f nd F . In this case, we try to f nd the laws governing systems from the knowledge of relation between in the inputs and outputs. The direct problems can be treated relatively easily. Inverse problems and identi f cation problems are relatively di cult to solve and form the central theme of the numerical analysis. Once we understand the generalized concepts of vector spaces, norms, oper- ators etc., we can see that the various inverse problems under consideration are not fundamentally di f erent. For example, Linear algebraic equations : X R n (5.5) A x = b can be rearranged as (5.6) F ( x )= A x b = 0
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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_21 - 44 2....

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