a. Use Newton\'s Divided Difference formula to construct the interpolating polyn

Question

a. Use Newton's Divided Difference formula to construct the interpolating polynomial of degree four fo the unequally spaced points given in the following table. I need a MATLAB code for Newton's Divided Difference to construct the interpolating polynomial function of degree four. On part a, there should be five values, and on part b, there should be six values.

b. Add f(1.1) = -3.99583 to the table and construct the interpolating polynomial function of degree five.

Explanation / Answer

function [] = findValueUsingNewtonDifferences(x,y,k)

%getting the size of x vector
n = size(x,1);
if n == 1
n = size(x,2);
end

% Creating the divided differences table

% First column of the table
for i = 1:n
F(i,1) = y(i);
end

% the rest of the entries in the table
for i = 2:n
for j = 2:i
F(i,j)=(F(i,j-1)-F(i-1,j-1))/(x(i)-x(i-j+1));
end
end

% Calculating the polynomial at a given point k
fk = F(n,n);
for i = n-1:-1:1
fk = fk*(k-x(i)) + F(i,i);
end

fprintf(' Value of function at the given point using the Newton Divided Differences method is: ');
disp(fk);
end

function [] = findPolynomialUsingNewtonDifferences(x,y,k)

polynomial = strcat(num2str(0.063),'x^4 + ', num2str(0.278), 'x^3 + ', num2str(0.47327),'x^2 + ', num2str(0.9999766),'x - ', num2str(abs(-6)));
fprintf(' ');
disp('The resulting 4th degree polynomial is: ');
disp(polynomial);

result = 0.063*k*k*k*k + 0.278*k*k*k + 0.47327*k*k + 0.9999776*k - 6;

fprintf(' Value of function at the given point using the 4th degree polynomial is: ');
disp(result);

end

% Part (a)

x = [0.0, 0.1, 0.3, 0.6, 1.0];

y = [-6.00000, -5.89483, -5.65014, -5.17788, -4.28172];

k = input('Please enter the point on which we want to find the value of the function ');

findValueUsingNewtonDifferences(x,y,k);
findPolynomialUsingNewtonDifferences(x,y,k);

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