Error: Matrix dimensions must agree.

% dening data points, vectors X and Y
X_VALUES=[0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5];
Y_VALUES=[0 0.247466462 0.881373587 1.550157957 2.094712547 2.532068064 2.893443986 3.200334942 3.466711038 3.70191108 3.912422766];
% dening x in range 0 to 5 with total 100 values
x = linspace(0,5,100);
ls = lagrange_self(X_VALUES,Y_VALUES,x);
sp = spline(X_VALUES,Y_VALUES,x);
plot(X_VALUES,Y_VALUES,'O',x,ls,'.',x,sp,'-')
title("Interpolating curves");
legend('Original','Cubic Polynomial Lagrange interpolating','Cubic Spline Interpolation')

% Calculate total error
% error for polynomal interpolation
ls = lagrange_self(X_VALUES,Y_VALUES,x);
% error

I get the 'Matrix dimensions must agree.' error on line 16

sp = sum(sqrt((Y_VALUES-ls).^2));
% displaying difference
fprintf("Total error for Cubic Spline Interpolation is %f\n",sp);
% error
s_cubic = sum(sqrt((Y_VALUES-y_cubic).^2));
% displaying difference
fprintf("Total error for Cubic Polynomial Lagrange interpolating is %f\n",s_cubic);

function v = lagrange_self(x,y,u)
n = 4;
v = zeros(size(u));
for k = 1:n
    w = ones(size(u));
    for j = [1:k-1 k+1:n]
        w = (u-x(j))./(x(k)-x(j)).*w;
    end
    v = v+w*y(k)
end
end

Thank you in advance for your help

Answer 1

[Cris LaPierre]

Y_VALUES is a 1x11 matrix while ls is 1x100. In order to subtract them, they must either both have the same size, or one must be a scalar (single number). Because they are not, MATLAB can't subtract them, and you get this error message.

The simplest fix is create to have the same number of points as Y_VALUES.

x = linspace(0,5,length(Y_VALUES));

[Kutlu Yigitturk]

Things to do is indicated as follows.

• Use Lagrange interpolating polynomial method and cubic spline interpolation to evaluate the function f(x) at 100 equally spaced points in the interval [0,5]. Use cubic polynomial for Lagrange’s method as well. The points to be used in interpolations should include first and last point (0 and 5), other two points should be chosen such that those points would represent significant change in f(x). Show the plots for Lagrange’s method, cubic spline and the given data in one graph. Discuss which method is better.
• Calculate the total error for both methods by using the following formula. Here yi is the given y value for xi , and f(xi) is the value of the interpolating function at point xi.
• 

So I cannot apply a solution like you explained. I must use ''x = linspace(0,5,100);'' like this. I would appreciate if there is any other solution you can suggest.

[Cris LaPierre]

It looks like you don't compute the error using every point. Just the points that correspond to .