Spline: Calculation Excel

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

Equation for i=3: h2*z2 + 2*(h2+h3)*z3 + h3*z4 = 6*(slope3 - slope2) → 2*z2 + 2*(2+3)*z3 + 3*0 = 6*(1 - (-0.5)) → 2*z2 + 10*z3 = 9 spline calculation excel

Slopes: =(B3-B2)/C2 → 1, =(B4-B3)/C3 → -0.5, =(B5-B4)/C4 → 1 For (n=4) points, we solve for (z_2, z_3) ((z_1 = z_4 = 0)). [ S(x) = a + b(x-x_i) + c(x-x_i)^2