Prove that every continuous piecewise affine function based on the mesh points x0 where (a) What are
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where
(a) What are the values of a and b?
(b) Write the hat function (11.168) in the form (11.179) .
(c) Write the piecewise affine interpolant constructed in Exercise 11.6.12(c), in the form (11.179) .
Remark: The multidimensional version of (11.179) , in which the absolute value is replaced by the Euclidean norm ||x||, is the simplest of a powerful new class of multivariate interpolation schemes known as radial basis functions, [9].
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