I try to understand the cubic interpolation for my studies. The following website says " (1) The four equations above can be rewritten to this (2):" but how? Can anyone explain me the the necessary steps?!
from (1)
f(0) = d
f(1) = a + b + c + d
f'(0) = c
f'(1) = 3a + 2b + c
to (2)
a = 2f(0) - 2f(1) + f'(0) + f'(1)
b = -3f(0) + 3f(1) - 2f'(0) - f'(1)
c = f'(0)
d = f(0)
Chris
\begin{align} 2f(0) - 2f(1) + f'(0) + f'(1) &= 2d - 2(a+b+c+d) + c + 3a+2b+c = a \\ -3f(0) + 3f(1) - 2f'(0) - f'(1) &= -3d + 3(a+b+c+d) - 2c - (3a+2b+c) = b \end{align}