hmwk_4_2010

hmwk_4_2010 - UNIVERSITY OF NOTRE DAME Department of Civil...

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UNIVERSITY OF NOTRE DAME Department of Civil Engineering and Geological Sciences CE 30125 October 12, 2010 J.J. Westerink Due: October 26, 2010 Homework #4 Background: Hermite Interpolation exactly matches both a set of functional values as well as a set of first and possibly higher order derivatives. We note that we must set up a polynomial function that has the same number of terms as we have constraints that we must enforce. While typically we set up Hermite interpolators that enforce functional values and derivatives at all nodes (or interpolation points), we can also have the situation where we are missing data at some of the nodes (for example Problem 1), in which case we simply reduce the degree of the polynomial (again simply by matching the total number of contraints). Note that in order to find the Hermite interpolation function, we simply define the polynomial and then enforce the constraints. In order to find the Hermite Basis functions , we simply factor out the functional values and the derivative values, leading to the so called basis functions. We have a basis function for each specified func-
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hmwk_4_2010 - UNIVERSITY OF NOTRE DAME Department of Civil...

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