First Semester in Numerical Analysis with Julia, 2020a

CHAPTER 3. INTERPOLATION 118
end
end
for i in 1:m
a[2i-1]=y[i]
a[2i]=y[i]
end
for i in reverse(collect(2:m)) # computes the first divided
#differences using derivatives
a[2i]=yprime[i]
a[2i-1]=(a[2i-1]-a[2i-2])/(z[2i-1]-z[2i-2])
end
a[2]=yprime[1]
for j in 3:l #computes the rest of the divided differences
for i in reverse(collect(j:l))
a[i]=(a[i]-a[i-1])/(z[i]-z[i-(j-1)])
end
end
return(a)
Out[2]: hdiff (generic function with 1 method)
Let’s compute the divided differences of Example 62.
In [3]: hdiff([-1.5, 1.6, 4.7],[0.071,-0.029,-0.012],
[1,-1,1])
Out[3]: 6-element Array{Float64,1}:
0.071
1.0
-0.33298647242455776
0.006713436944043511
0.015476096374635765
-0.005196626333767283
Note that in the hand-calculations of Example 63, where two-digit rounding was
used, we obtained 0.0065 as the first third divided difference. In the Julia output above,
this divided difference is 0.0067.