Spline Calculation Excel Site

[ S(x) = a + b(x-x_i) + c(x-x_i)^2 + d(x-x_i)^3 ]

For (i = 2, 3, ..., n-1). With (z_1 = z_n = 0). Let’s interpolate with the points: (1, 2), (2, 3), (4, 2), (7, 5) Step 1: Organize Data | A | B | |---|---| | x | y | | 1 | 2 | | 2 | 3 | | 4 | 2 | | 7 | 5 | Step 2: Calculate Intervals and Slopes | C (h) | D (slope) | |---|---| =A3-A2 → 1 =A4-A3 → 2 =A5-A4 → 3 spline calculation excel

Equation for i=2: h1*z1 + 2*(h1+h2)*z2 + h2*z3 = 6*(slope2 - slope1) → 1*0 + 2*(1+2)*z2 + 2*z3 = 6*(-0.5 - 1) → 6*z2 + 2*z3 = -9 [ S(x) = a + b(x-x_i) + c(x-x_i)^2

Solve in Excel: Use and MMULT or manual algebra. (x=1 to 2, h=1): a = 2 b = (3-2)/1 - 1/6*(2 0 + (-1

(x=1 to 2, h=1): a = 2 b = (3-2)/1 - 1/6*(2 0 + (-1.92857)) = 1 - (1/6) (-1.92857) = 1 + 0.32143 = 1.32143 c = 0/2 = 0 d = (-1.92857 - 0)/(6*1) = -0.32143