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

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Kalasagarreddi Kottakota
评论： Bruno Luong 2022-3-30
How to find an expression for using matlab, so that the below equation equals to zero.

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Bruno Luong
Bruno Luong 2022-3-27
编辑：Bruno Luong 2022-3-27
Ran in:
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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Bruno Luong
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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