Prove that a cubic B spline, as defined in Exercise 5.5.76, solves the dilation equation (9.138) for
Question:
Prove that a cubic B spline, as defined in Exercise 5.5.76, solves the dilation equation (9.138) for c0 = c4 = 1/8, c1 = c3 = 1/2, c2 = 3/4.
Data From Exercise 5.5.76
A bell-shaped or B-spline u = β(x) interpolates the data
(a) Find the explicit formula for the natural B-spline and plot its graph.
(b) Show that β(x) also satisfies the homogeneous clamped boundary conditions u′(−2) = u′(2) = 0.
(c) Show that β(x) also satisfies the periodic boundary conditions. Thus, for this particular interpolation problem, the natural, clamped, and periodic splines happen to coincide.
(d) Show that
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: