First Semester in Numerical Analysis with Julia, 2020a

CHAPTER 5. APPROXIMATION THEORY 183
end
for j in 1:m
sum=sum+x[j]^(i-1)
end
p[i]=sum
end
# We next compute the upper triangular part of the
# coefficient matrix A, and its diagonal
for k in 1:d
for j in k:d
A[k,j]=p[k+j-1]
end
end
# The lower triangular part of the matrix is defined using
# the fact the matrix is symmetric
for i in 2:d
for j in 1:i-1
A[i,j]=A[j,i]
end
end
a=A\b
Out[2]: leastsqfit (generic function with 1 method)
Here is the data used to produce the first plot of the chapter: Arya’s data:
In [3]: xd=[1,2,3,4,5,6];
yd=[3,5,9.2,11,14.5,19];
We fit a least squares line to the data:
In [4]: leastsqfit(xd,yd,1)
Out[4]: 2×1 Array{Float64,2}:
-0.7466666666666616
3.1514285714285704