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Unformatted text preview: cient. In order to work with these sets of generalized vectors, we need various algebraic and geometric structures on these sets, such as norm of a vector, angle between two vectors or convergence of a sequence of vectors. To understand why these structures are necessary, consider the fundamental equation that arises in numerical analysis (1.1) F ( x ) = where x is a vector and F ( . ) represents some linear or nonlinear operator, which when operates on x yields the zero vector . In order to generate a numerical approximation to the solution of equation (6.2), this equation is further transformed to formulate an iteration sequence as follows (1.2) x ( k +1) = G x ( k ) ; k = 0 , 1 , 2 , ...... where x ( k ) : k = 0 , 1 , 2 , ...... is sequence of vectors in vector space under consideration. The iteration equation is formulated in such a way that the solution x of equation ( 1.2 ), i.e. x = G [ x ] 23...
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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.
 Fall '11
 Mr.Shaw
 Chemical Engineering

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