How to solve the following type of equation that includes summation in matlab?

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How to find an expression for using matlab, so that the below equation equals to zero.

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Bruno Luong
Bruno Luong le 27 Mar 2022
Modifié(e) : Bruno Luong le 27 Mar 2022
Assuming
H_m and t_m are stored in (1 x M )arrays
% Dummy test data
M = 10;
H = rand(1,M);
t = rand(1,M);
P = sum( abs(H(:)).^2 .* [-ones(M,1) +3*t(:) -3*t(:).^2 +t(:).^3]);
t0 = roots(P)
t0 =
0.2914 + 0.3069i 0.2914 - 0.3069i 0.3144 + 0.0000i
sum(abs(H).^2 .* (t - t0).^3, 2)
ans =
1.0e-15 * -0.2845 + 0.1978i -0.2845 - 0.1978i 0.1162 + 0.0000i
  10 commentaires
Kalasagarreddi Kottakota
Kalasagarreddi Kottakota le 30 Mar 2022
@Bruno Luong Thanks,
I dont see any mistake in the matlab expression. Could you please elaborate your commment.
Bruno Luong
Bruno Luong le 30 Mar 2022
Elaborate what? Your orginal equation you post seems fishy to me, not the MATLAB implementation of your equation.
Another fischy fact : the expression only have sum of strictly positive quantities, you cannot expect there is a real root of it. Something is wrong with the maths/physics where you derive the expression/equation.

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