SOLVED:Suppose that the natural cubic spline s2 interpolates the function f: x ↦x^3 on the interval [0,1], the knots being equally spaced, so that xi=i h, i=0,1, …, m, with h=1 / m, m ≥2. Write down the equations which determine the quantities σi . If the two additional conditions are σ0=σm=0, show that these equations are not satisfied by σi=f^''(xi), i=1, …, m-1, so that s2 and f are not identical. If, however, these two additional conditions are replaced by σ0=f^''(0), σm=f^''(1), show that σ
SOLVED:Suppose that the natural cubic spline s2 interpolates the fu…
Feb 2, 2022
numerade.com
SOLVED:Suppose you are asked to construct a clamped cubic spline interpolating the following set of data: i 0 1 2 3 4 5 6 7 x 1.2 1.4 1.6 1.67 1.8 2.0 2.1 2.2 f(x) 4.561 5.217 5.634 5.935 6.562 6.242 5.812 5.367 The function underlying these data points is unknown, but clamped cubic splines require interpolation of the first derivative of the underlying function at the end points x0=1.2
SOLVED:Suppose you are asked to construct a clamped cubic spline i…
2 months ago
numerade.com
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