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program for lagranges interpolation method using single for loop

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PJS KUMAR
PJS KUMAR 2018-8-23
回答： Geoff Hayes 2018-8-23
how to program for lagranges interpolation method using single for loop
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Geoff Hayes
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
PJS KUMAR 2018-8-23
yes, for performance reasons can we write the program by using vector operations.

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回答（1 个）

Geoff Hayes
Geoff Hayes 2018-8-23
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!

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