PPT Slide

Construction of Cubic Splines

(a) Determine the derivative coefficients (m):

hk-1mk-1 + 2mk(hk-1+hk) + hkmk+1 = 6(dk - dk-1) (5.2)

for k = 1, 2, ..., N-1

where m0 = S”(xk), hk = xk+1 - xk, dk = (yk+1 - yk)/ hk

(b) Spline coefficients:

sk,0 = yk sk,1= dk - (2mk + mk+1)hk/6

sk,2= mk/2 sk,3= (mk+1 - mk)/(6hk) (5.3)

(c) Cubic polynomial:

Sk(x)=sk,0+sk,1(x-xk)+sk,2(x - xk)2+sk,3(x - xk)3 (5.4)

for

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