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

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Kalasagarreddi Kottakota 2022-3-27

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https://ww2.mathworks.cn/matlabcentral/answers/1681799-how-to-solve-the-following-type-of-equation-that-includes-summation-in-matlab

评论： Bruno Luong 2022-3-30

采纳的回答： Bruno Luong

How to find an expression for

using matlab, so that the below equation equals to zero.

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Bruno Luong 2022-3-27

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https://ww2.mathworks.cn/matlabcentral/answers/1681799-how-to-solve-the-following-type-of-equation-that-includes-summation-in-matlab#answer_928079

编辑：Bruno Luong 2022-3-27

在 MATLAB Online 中打开

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

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Kalasagarreddi Kottakota 2022-3-30

@Bruno Luong Thanks,

I dont see any mistake in the matlab expression. Could you please elaborate your commment.

Bruno Luong 2022-3-30

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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