how to write a alternatives codes to calculating a Lagrange's interpolation polynomial

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Bhavya
Bhavya 2024-4-15
回答： Aastha 2024-9-18
clc
clear all
syms t
x=input('enter list of x values:');
y=input('enter list of y values:');
X=input('enter X for which value of y is to be calculated:');
n=length(x);
s=0;
for i=1:n
L=1;
for j=1:n
if j~=i
L=L*(t-x(j))/(x(i)-x(j));
end
end
s=s+y(i)*L;
end
this is the sample code to run the program to calculating lagrange interpolation polynomial in matlab is their any alternative ways to write code let me know

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回答（1 个）

Aastha
Aastha 2024-9-18
Hi @Bhavya,
I find that you want to write a code to calculate Lagrange’s interpolation polynomial.
You can efficiently implement the Lagrange polynomial using matrices by vectorizing computations to calculate and sum all basis polynomials simultaneously using a dot product. You may refer to the steps mentioned below to do so:
1. Begin by ensuring the input weights vector y and node vector x are row vectors. Then, determine the number of basis polynomials. The code snippet below illustrates an example:
if iscolumn(x)
x = x';
end
if iscolumn(y)
y = y';
end
n = length(x); %Here n is the number of basis polynomials
For more information on “iscolumn” and “length” function, you may refer to the following MathWorks documentation:
2. Then, generate a grid of node vector values to evaluate all basis polynomials simultaneously. You can refer to the code snippet below to generate a grid of node vector values:
x_grid = repmat(x, n, 1);
You may refer to the MathWorks documentation for any more information on “repmat” function. Here is the link to it:
https://www.mathworks.com/help/matlab/ref/repmat.html
3. Next, you can calculate the numerators for all basis polynomials and compute their weighted sum using vectorized MATLAB operations. The code snippet below illustrates an example to do so:
s = sum(transpose(y) .* prod(((x - x_grid) .* (ones(n, n) - eye(n)) + eye(n)) ./ ...
(transpose(x - transpose(x_grid)) + eye(n)), 2));
For any more information on “sum” and “transpose” functions, you may refer to link of MathWorks documentation whose link is mentioned below:
This approach streamlines the computation of Lagrange polynomials using matrices and vectorized MATLAB operations.
Hope this helps!

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