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# set0 - \$ Set 0 Overview Kyle A Gallivan Department of...

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a39 a38 a36 a37 Set 0: Overview Kyle A. Gallivan Department of Mathematics Florida State University Foundations of Computational Math 2 Spring 2011 1

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a39 a38 a36 a37 Overview Basic Problems Interpolation of a function Approximation of a function Application of Techniques Numerical differentiation of a function Numerical quadrature (evaluation of a definite integral) Numerical integration (solution of an ODE: IVP or BVP) 2
a39 a38 a36 a37 Interpolation and Approximation Given a function f ( x ) in some form: symbolically/analytically discrete values of f and possibly some of its derivatives Given assumptions about f ( x ) smoothness periodic Given a class of functions S and a parameterization. Find g ∈ S that satisfies some constraints, e.g., g agrees at specified points with f and/or its derivatives g is closest to f using some measure 3

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a39 a38 a36 a37 Discrete Function Values For some problems the starting point data comprises discrete values ( x i , y i )
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