How to code this problem?

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!

[James Tursa]

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]

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)

Answer 1

[James Tursa]

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)

[John Amitage]

The program gives me:

X =

  4×1 cell array

    {1×1 sym   }
    {0×0 double}
    {0×0 double}
    {0×0 double}
    

How can I convert it?

Thank You :D

[James Tursa]

What is the A variable you are using? What version of MATLAB are you using?

[John Amitage]

My Matlab version is R2018a

[James Tursa]

And A?

[John Amitage]

Oh I am sorry, may I ask you what is "A variable"?

[James Tursa]

Look at your original post, you have this variable

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

I am asking you what "A" variable you are using with the code I have given you. The code works for me as I have demonstrated.

[John Amitage]

I copied your code but without the semicolon because the program display nothing if it's there

[James Tursa]

So, what is the problem? It looks like the code works for you. What does this show after you run the code:

X{1}
X{2}
X{3}
X{4}

Aren't those the polynomials you want?

[John Amitage]

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

Thank you and have a good day !

[James Tursa]

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.