Given x0 1 x1 4 3 x2 5 3 x3 2 find the clamped spline

Given x0 = 1, x1 = 4 /3 , x2 = 5 /3 , x3 = 2 find the clamped spline agreeing with f(x) at these values.

Solution

given x₀=1, x₁=4/3, x₂=5/3, x₃=2

here x₀<x₁<x₂<x₃

_{so these are satisfying spline agreeing with f(x)}

_{on each of the interval taken as [1,4/3], 4/3,5/3], [5/3,2]}

_{where f(x) is a polynomial of degreee \'3\'}

_{and f(x), f\'(x),f\"(x) are all continuous functions in these intervals}

_{and f(xi})= y_i