Let 0(x) denote the 5-spline function of Exercise 11.4.23. Assuming n > 4, let P denote the
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where m denotes the integer part of n/2. form a basis for Pn
(b) Graph the basis periodic 5-splines in the case n = 5.
(c) Let u(x) denote the periodic spline interpolant for the data values y0,... , yn-1. Explain how to write u(at) = a0β0 +--------+ αn - I βn-1 in terms of the 5 splines by solving a linear system for the coefficients ao..........a"_i.
(d) Write the periodic spline with y0 = y5 = 0, y1 - 2, y2 = 1, y3 = -1. y4 = -2, as a linear combination of the periodic basis 6- splines B0(x)..........54(jr). Plot the resulting periodic spline function
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