program for lagranges interpolation method using single for loop

Question

0 个投票

how to program for lagranges interpolation method using single for loop

4 个评论
显示 2更早的评论隐藏 2更早的评论

Geoff Hayes 2018-8-23

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 2018-8-23

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

Answer 1

Geoff Hayes 2018-8-23

0 个投票

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!