Question

Create a MATLAB function to perform Lagrange Interpolation. Your function will be used as illustrated below:

>> ya = Lagrange(x, y, a)

where "x" is a vector of ? independent data values, "y" is a vector of ? dependent function values corresponding to "x", "a" is an arbitrary value of "x" for which you want to know the Westimate of "y", and "ya" is the estimate of the function at x=a. Print an error message and exit the function if the size of the "x" and "y" vectors are not compatible. Hints: MATLAB built-in function "length()" can be used to return the number of elements in a vector, and built-in function "error()" will print an error message and exit the function. The following table lists values of the Bessel function of the first kind, of order zero.

? 1.0 , 1.3 , 1.6 , 1.9 , 2.2

?(?) 0.7651977 , 0.6200860 , 0.4554022 , 0.2818186 , 0.1103623

In the Command Window, use the commands needed to create the "x" and "y" vectors, and then use your MATLAB function to obtain the answer to the following question: What is the estimated value of the function at ? = 1.5? When complete, your MATLAB Workspace should include the input and output variables.

Answer 1

`Hey,

Note: Brother in case of any queries, just comment in box I would be very happy to assist all your queries

clear all
clc
x=[1.0 , 1.3 , 1.6 , 1.9 , 2.2];
y=[0.7651977 , 0.6200860 , 0.4554022 , 0.2818186 , 0.1103623];
disp('Value at x=1.5 is')
[yhat]=Lagrange(x,y,1.5)
function [yhat]=Lagrange(x,y,interpx)
if(length(x)~=length(y))
error('x and y are not compatible');
end
X=x;
f=y;
x=interpx;

l=0;
for i=1:length(X)
li=1;
for j=1:length(X)
if i~=j
li=(li).*((x-X(j))/(X(i)-X(j)));
end
end
l=(l)+((li)*f(i));
end
yhat=l;
  
end

Kindly revert for any queries

Thanks.