ok, I'm trying to make a Newton's forward & backwards divided difference formula in c++ and the damn thing doesn't work because I don't know how to get the values of s. The book sucks in explaining how to get s and stuff.
I do know the original s is x = x0- sh.
I need help determining the other s values, example.
n xn f[xn] 1st DivDiff 2nd Div Diff 3rd DivDiff 4th DivDiff
0 1 0.7651977 -0.4837057 -0.1087339 0.0658784 0.001825103
1 1.3 0.620086 -0.548946 -0.04944333 0.06806852
2 1.6 0.4554022 -0.578612 0.01181833
3 1.9 0.2818186 -0.571521
4 2.2 0.1103623
s = 0 .3333333
h = .3
I know to get the forward divided difference of 1.1 using all 5 points, I do
0.7651977 + (s)(h)(-0.4837057) + ( (s+1)/2) * h^2 * -0.1087339
but it is incomplete because I don't know how I don't know the formula for getting "s" for the rest of the function.
I do know the original s is x = x0- sh.
I need help determining the other s values, example.
n xn f[xn] 1st DivDiff 2nd Div Diff 3rd DivDiff 4th DivDiff
0 1 0.7651977 -0.4837057 -0.1087339 0.0658784 0.001825103
1 1.3 0.620086 -0.548946 -0.04944333 0.06806852
2 1.6 0.4554022 -0.578612 0.01181833
3 1.9 0.2818186 -0.571521
4 2.2 0.1103623
s = 0 .3333333
h = .3
I know to get the forward divided difference of 1.1 using all 5 points, I do
0.7651977 + (s)(h)(-0.4837057) + ( (s+1)/2) * h^2 * -0.1087339
but it is incomplete because I don't know how I don't know the formula for getting "s" for the rest of the function.
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