Question

1. Write a function to evaluate a Lagrange interpolating polynomial at a given value z. Given you have n arbitrary points (xi ; yi) to start with to build the polynomial. Use the algorithm provided for this assignment. To receive full marks you must: • Name of your function must be Lpoly5 • Use the variables in the order they are described in the Algorithm handout for this lab. • Submit the .m file for your function with the correct name. To receive full marks, your function, Lpoly5, but evaluate a polynomial of created from an arbitrary number of starting points (xi ; yi) (n points). This will be tested with data not provided to students. As a test case, you can use the points from the lab handout. Do not submit your results of this case. It is for your assistance only.

Answer #1

function Lpoly5

clear all;

clc;

%n=input('Enter the value of n: ');

%disp('Enter value of x: ')

%for i=1:n

% x(i)=input('x: ');

%end

%disp('Enter value of x: ')

%for i=1:n

% y(i)=input('y: ');

%end

x= [1,2,0,3]

y= [3,2,-4,5]

syms z

sum=0;

d=1;

%z=input('Enter value of z: ')

z=8

fprintf('Coefficients of polynomial by Langrange method:\n');

for i=1:4

for j=1:4

if i~=j

d=d*((z-x(j))/(x(i)-x(j)));

end

sum=sum+d*y(i);

end

fprintf('L%d',i-1);

d

end

disp('Lagrange interpolating polynomial at a given value z is: ')

sum

% This program calculates the Lagrange interpolating
polynomial of a given % xp and returns the value
clc, clear all;
format short;
x=[0 20 40 60 80 100];% This string can be filled by
Matlab
f_x=[26.0 48.6 61.6 71.2 74.8 75.2]; % You can create a
separate function to fill
f_x automatically
n=length(x)-1;
xp=input('Enter a value xp between 0 and 100: '); P_x=0;
for i=1:n+1
L_k=1;
for j=1:n+1
if j~=i L_k=L_k*(xp-x(j))/(x(i)-x(j));
end end
P_x=P_x+f_x(i)*L_k;
end
disp ('The polynomial P_xp at...

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