How to code this problem?

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John Amitage 2019-5-10

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https://ww2.mathworks.cn/matlabcentral/answers/461389-how-to-code-this-problem

关闭： MATLAB Answer Bot 2021-8-20

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For example,

I got

A=[ 1 2 4 5 1 .......]

I want to calculate:

X1=(x-2)(x-4)(x-5)(x-1).....
X2=(x-1)(x-4)(x-5)(x-1)....
X3=(x-1)(x-2)(x-5)(x-1)....

And so on

So how can I code it on Matlab?

Thank you very much!

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James Tursa 2019-5-10

What have you done so far? What specific problems are you having with your code? Are you after a symbolic result, or a numeric result for a specific value of x?

John Amitage 2019-5-10

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Hi, thank you for your answer

I've tried

syms x
X=[1 2 3]
n=size(X,2)
A=1
for i=2:n
    A=A*(x-X(i))
end

And it gives me A=(x-2)(x-3)

So I'm finding a way to make the program also gives me B=(x-1)(x-3) and C=(x-1)(x-2) and generalize it so when I input any vector X with any n=size(X,2) it can give me the full answer.

Specifically, I'm doing Lagrange Interpolation

Thank you

(sorry for my English)

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回答（1 个）

James Tursa 2019-5-10

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/461389-how-to-code-this-problem#answer_374461

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E.g.,

syms x
A = [1 2 4 5];
n = numel(A);
P = prod(x-A);
X = cell(n,1);
for k=1:n
    X{k} = P / (x-A(k));
end

This gives a cell array

>> X{1}
ans =
(x - 2)*(x - 4)*(x - 5)
>> X{2}
ans =
(x - 1)*(x - 4)*(x - 5)
>> X{3}
ans =
(x - 1)*(x - 2)*(x - 5)
>> X{4}
ans =
(x - 1)*(x - 2)*(x - 4)

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John Amitage 2019-5-10

ahh I understand now, i'm so sorry for taking your time :D

Thank you and have a good day !

James Tursa 2019-5-10

No problem! Note that it is easy to generalize this to an arbitrary sized "A" variable by using a cell array. It would be horrendous to try and implement this with named variables X1, X2, etc.

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