{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chemical Engineering Hand Written_Notes_Part_21

Chemical Engineering Hand Written_Notes_Part_21 - 44 2...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
44 2. FUNDAMENTALS OF FUNCTIONAL ANALYSIS Inverse Problems: Given operator F and y , fi 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 ff erential equations and integral equations are examples of this category Identi fi cation problems: Given operator x and y , fi nd F . In this case, we try to fi 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 fi 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 ff 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}