Find roots of quadratic matrix polyunomial

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Andrea Baleani
Andrea Baleani 2023-7-13
回答： Malay Agarwal 2023-7-13
I'd like to solve the following equation where are square complex matrices.

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回答（1 个）

Malay Agarwal
Malay Agarwal 2023-7-13
Ran in:
Hi @Andrea Baleani,
Please try the following code. This uses the fsolve function to solve the equation numerically.:
% Define the matrix A as a complex matrix
A = complex(randn(5,5), randn(5,5));
% Define the equation function handle
eq = @(X) A*X^2 + X + A;
% Define the initial guess for X
x0 = complex(randn(5, 5), randn(5, 5));
% Solve the equation for X using fsolve
X_solution = fsolve(eq, x0);
Solver stopped prematurely. fsolve stopped because it exceeded the function evaluation limit, options.MaxFunctionEvaluations = 2.500000e+03.
% Display the solution for X
disp('Solution for X:');
Solution for X:
disp(X_solution);
10.4364 -14.8118i -0.6416 -10.9103i 9.4393 + 6.4624i 0.8966 + 5.5707i -1.4579 +11.0934i -6.2341 -22.7503i -18.8040 + 8.5239i 25.2421 -21.1322i -20.1716 + 8.5526i -1.6253 + 6.1362i 20.2211 - 1.4709i -21.2125 + 7.0483i 35.1446 + 2.8148i -45.9995 -20.6433i -21.7074 -13.8708i 23.3683 - 2.0332i -13.0695 +15.8339i 30.7822 - 5.9025i -54.1409 - 4.7549i -30.4751 - 7.9421i -2.9071 -10.0220i -1.5065 -36.7388i -4.2081 +29.9107i 46.4775 -17.6436i 27.6587 + 6.8325i

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