program for lagranges interpolation method using single for loop

how to program for lagranges interpolation method using single for loop

[Geoff Hayes]

PJS - what have you tried so far? Please describe what you have attempted and discuss any errors or bugs that you are observing with your code. Right now, your question (or request) is much too vague...

[PJS KUMAR]

function sum=Lagrange(x,y,a)
sum = 0;
format shortG

for i = 1:length(x)
    u = 1;
    l = 1;
    for j = 1:length(x)
        if j ~= i
            u = u * (a - x(j));
            l = l * (x(i) - x(j));
        end
    end
    sum= sum + u / l * y(i);
end

[Geoff Hayes]

Please rename your local variable sum since it conflicts with the MATLAB built-in function of the same name.

Out of curiosity, why do you want to eliminate the inner for loop? For performance reasons?

[PJS KUMAR]

yes, for performance reasons can we write the program by using vector operations.

Answer 1

[Geoff Hayes]

PJS - if we assume that x is a vector/array then u is simply

 u = (a - x(1)) * (a - x(2)) * ... * (a - x(i-1)) * (a - x(i+1)) * ... * (a - x(n));

where n is the number of elements in x. If this is true, then couldn't we do something like

 for i = 1:length(x)
    u = 1;
    l = 1;
    xt = x;
    xt(i) = []; % remove the ith element
    u = prod(a - xt);
    % etc.
 end

We use prod to calculate the product of all elements in the array. Similarly, for l

 l = (x(i) - x(1)) * (x(i) - x(2)) * ... * (x(i) - x(i-1)) * (x(i) - x(i+1)) * ... * (ax(i) - x(n));

which means that the above can be replaced with

 l = prod(x(i) - xt));

Try the above and see what happens!