First Semester in Numerical Analysis with Julia, 2020a

CHAPTER 3. INTERPOLATION 130
end
end
return(a)
Out[4]: diff (generic function with 1 method)
In [5]: function newton(x::Array,y::Array,z)
m=length(x) # here m is the number of data points, not the
# degree of the polynomial
a=diff(x,y)
sum=a[1]
pr=1.0
for j in 1:(m-1)
pr=pr*(z-x[j])
sum=sum+a[j+1]*pr
end
return sum
end
Out[5]: newton (generic function with 1 method)
Here is the code that computes the cubic spline, Newton interpolation, and plot
them.
In [6]: using LaTeXStrings
xaxis=-5:1/100:5
f(x)=1/(1+x^2)
runge=f.(xaxis)
xi=collect(-5:1:5)
yi=map(f,xi)
CubicNatural(xi,yi)
naturalspline=map(z->CubicNaturalEval(z,xi),xaxis)
interp=map(z->newton(xi,yi,z),xaxis) # Interpolating polynomial
# for the data
plot(xaxis,runge,label=L"1/(1+x^2)")
plot(xaxis,interp,label="Interpolating poly")
plot(xaxis,naturalspline,label="Natural cubic spline")