Given data points (xo, uo). .........(xn un) with x, ‰ , i ‰  j, prove that there is a unique continuous piecewise affine interpolant u = f(x), so u = 0..........n.
(a) Prove that the piecewise affine interpolant can be written in the form

where φi denotes the hat function (11.167).
(b) Write down and graph the piecewise affine in-terpoiant for the following data:

Transcribed Image Text:

xi u 2 3 6 11