Question

2. Write a question for Newton-divided difference interpolation. Then, solve it theoretically. After solving it, write a MATLAB code for this question which returns either an estimation for a value or the polynomial coefficients of ',x1, x²,..., respectively, Instructions: . You do not need to create built-in function. You may study on a script, • You have already known your table, which is written as a question. Using this table, write a code which returns either an estimation for a value or the polynomial coefficients of zº,r', r, ... respectively. The choice is up to you. But, you should note what you search for on the question.

Answer 1

SOLUTION:-

clc%clears screen

clear all%closes history

close all%closes all files

format long

X= 0:0.2:1;

Y= exp(-X).*cos(X);

x=0:0.01:1;

y=newton_interp(X,Y,x)

plot(x,yX,Y'0');

function y= newton_interp(X,Y,x)

format long

a=x;

b=y;

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

[m,n]=size(a)

fx=0;

for l=1:n

%--------------calculating dividing diference-----------

s=0;

for i=1:l

p=1;

for k=1:l % Denomlnator part product

if(k~=j)

p=p*(a(j)-a(k));

end

end

s=s+b(J)/p;%summalation f(x)/product

end

%---------------------------------------------------------------------------------------

p=1;

for J=1:1-1%coefficlent part of f [...]

p=p.*(x-a(J)));

end

fx=fx+s.*p; %Polynomlal!

end

y=fx;

end

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