Numerical Analysis, Matlab computer programming (Matlab) (a) Write a Matlab func

Question

Numerical Analysis, Matlab computer programming

(Matlab) (a) Write a Matlab function that inputs , a vector of z-coordinates of data points (nodes); y, an array of y-coordinates of data points; n, the total number of data points; and z, one location on the x-axis. Have it output the value of the in terpolating polynomial for the data points, computed using Lagrange form, at z Write out or print out your function and turn it in (b) Use your program to approximate f(2) for the table of data 01 4 9 16 f(x)0123 4 Write out or print out your results and turn them in

Explanation / Answer

CODE:
The below function will Calculate the Lagrange polynomial interpolation.

function y = lagrange(x, pointx, pointy)
% x = vector of points where you want to interpolate
% pointx = vector of data values for x - axis
% pointy = vector of data values for y - axis
%
% If length of pointx and pointy are different, the function will return the NaN value
L = ones(n,size(x,2));
n = size(pointx,2);

if (size(pointx,2)~=size(pointy,2))
fprintf(1,'pointx and pointy dimensions are not same ');
y=NaN;
else
for i=1:n
for j=1:n
if (i~=j)
L(i,:)=L(i,:).*(x-pointx(j))/(pointx(i)-pointx(j));
end
end
end
y=0;
for i=1:n
y=y+pointy(i)*L(i,:);
end
end

It will return a vector y as the output. From the output y, we can get the y[2] value as desired for
second part of the problem.

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